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THE 

ELEMENTS OE HYDROLOGY 



BY 
ADOLPH F. MEYER, C.E., 

Member American Society of Civil Engineers 

Consulting Engineer 
Associate Professor of Hydraulic Engineering 
University of Minnesota 



FIRST EDITION 



NEW YORK 

JOHN WILEY & SONS, Inc. 

London: CHAPMAN & HALL, Limited 
1917 






Copyright, 1917, 

BY 

ADOLPH F. MEYER 



AUG 10 1917 



Stanbope flbress 

F. H. GILSON COMPANY 
BOSTON, U.S.A. 



©CLA470580 



PREFACE 

The science of hydrology, although it has received relatively little 
attention in the United States until recent years, has a wide field 
of application. It is fundamental to the solution of many prob- 
lems in water-power, water-supply, sewerage and sewage disposal, 
drainage, irrigation, navigation, and flood protection and pre- 
vention. Although basic to a large field of engineering science, 
hydrology itself is founded upon numerous other sciences, as well 
as upon a large body of physical data peculiar to itself. 

Although the material presented in the following pages represents 
considerable effort, it is far from complete, and only the urgent 
need for a book which should set forth at least the most impor- 
tant physical bases and applications of the fundamental prin- 
ciples underlying the science of hydrology, induced the author 
to prepare the material for publication at this time. 

The book is intended to be of assistance to professional men, 
teachers, and students of engineering. It has been prepared 
with the view of clearly setting forth fundamental data and con- 
siderations rather than of providing either a text or a reference 
book, and, of course, not a handbook. It will be years before 
the fundamental principles and facts underlying the science of 
hydrology have received sufficiently general acceptance to per- 
mit their condensation into handbook form. 

The data and computations presented in this book were pre- 
pared with the assistance of a paid office staff and are believed 
to be free from material discrepancies. While all totals and 
summaries of important data were checked, and many were 
double-checked, using the adding machine, the work of tabu- 
lating the tens of thousands of precipitation records, for example, 
was not duplicated, because the possibility of errors being made 



IV PREFACE 

in the compilations which could affect the final conclusions was 
so sniall as not to warrant the expense of the extra work. 

Endeavor has been made to acknowledge the source of all 
previously published data wherever these are first introduced. 
Valuable assistance was rendered and courtesies were extended 
by several Departments of the Government, particularly, the 
Weather Bureau, the Department of Agriculture, and the Geo- 
logical Survey; and also by the University of Minnesota, the 
American Society of Civil Engineers, Engineering News, En- 
gineering Record, and by numerous other publications and 
individuals. 

Acknowledgment is also due the author's assistants, Mr. 
George M. Shepard, Mr. E. Dow Gilman, Miss Edna Busse, 
Mr. W. J. von Eschen, and others, for loyal and capable service 
in the preparation of manuscript. Some of these assistants gave 
their undivided attention to this work for several months. 

The author also appreciates the work done by Prof. C. W. 
Nichols and Mr. M. W. Hewett in connection with the proof 
reading. 



adolph f. Meyer. 



Minneapolis, Minn., 
January, 1917. 



CONTENTS 



CHAPTER I 

Page 

INTRODUCTION 1 

Definition of Hydrology 1 

Present State of Hydrology 1 

Application of Hydrology 2 

Water as a Natural Resource 5 

The Subject Matter of Hydrology 5 

CHAPTER II 

THE ATMOSPHERE: ITS TEMPERATURE, PRESSURE AND 

CIRCULATION 9 

Use 9 

Composition 9 

Properties 11 

Amount of Water in Atmosphere 12 

Distribution of Water Vapor 12 

TEMPERATURE 13 

Source of All Heat 13 

Effect of Water Vapor on Solar Radiation 14 

Measurement of Solar Radiation 15 

Amount of Solar Radiation Received 15 

Refraction 18 

Temperature Data 19 

Thermometers 19 

Daily Mean 21 

Annual Variation 22 

Periodic Variation 23 

Extremes of Temperature 23 

Variation with Altitude 23 

Extending Short-term Records 27 

PRESSURE OF THE ATMOSPHERE 27 

Amount and Variation with Altitude 27 

High- and Low-pressure Areas 29 

Daily Variation in Pressure 29 

Synchronism of Various Phenomena 30 

v 



vi CONTENTS 

Page 

CIRCULATION OF THE ATMOSPHERE 34 

Wind Pressure 34 

Cause of Winds 35 

Wind Zones 35 

Periodic W T inds 36 

Non- Periodic Winds 36 

Anemometers 36 

Mean Wind Velocities in the United States 38 



CHAPTER III 

WATER: ITS VARIOUS STATES AND THEIR PROPERTIES 39 

Composition 39 

Physical Properties : . . 39 

Frazil 40 

Anchor Ice .'..., 41 

Elasticity 41 

Weight 41 

Steam 41 

Specific Heat '. 42 

Heat of Vaporization 42 

Heat of Fusion 42 

THE VAPOR OF WATER AND ITS CONDENSATION 43 

Characteristics of Water Vapor 43 

Vapor Pressure 43 

Distribution of Water Vapor 44 

Relation of Vapor Pressure to Weight of Vapor 44 

Change in Vapor Pressure with Temperature 45 

Dew-point Hygrometers 49 

Wet- and Dry-bulb Hygrometers 50 

Humidity 53 

Density of Air 53 

Specific Heat of Air 56 

Dynamic Cooling 61 

Stable and Unstable Air 62 

Effect of Vapor on Weight of Air 62 

CHAPTER IV 

PRECIPITATION: ITS OCCURRENCE AND DISTRIBUTION 64 

Dew and Frost 64 

Rain, Snow, etc 64 

Convective Precipitation 65 

Orographic Precipitation 65 

Cyclonic Precipitation 65 



CONTENTS Vll 

Page 

" Lows " 70 

" Highs " 70 

Thunderstorms 71 

Weather Forecasts 77 

Measurement of Precipitation 78 

Standard Rain Gage 78 

Tipping-bucket Gage 79 

Marvin Float Gage , 80 

Exposure of Rain Gage 80 

Measuring Snowfall 81 

Snow Surveys 85 

Variation of Character of Precipitation with Temperature . 86 

Ice Storms 87 

Variation of Precipitation with Latitude, Altitude, etc 88 

Irregular Occurrence in United States 89 

Mean Annual Precipitation 93 

Cycles in Annual Precipitation 93 

Relation Between Length of Record and Extremes of 

Annual Precipitation 110 

Maps of Probable Extremes of Annual Precipitation in 

United States Ill 

Monthly Precipitation 114 

Determination of True Monthly Mean 121 

Excessive Monthly and Daily Precipitation 122 

Typical Excessive Rainstorms 128 

Area Covered by Excessive Storms 139 

Estimating Probable Maximum Precipitation on Water- 
sheds 140 

Hourly Rates of Excessive Precipitation 144 

Index Map 150 



CHAPTER V 

EVAPORATION FROM WATER SURFACES 188 

The Water Cycle 188 

Evaporation Defined 190 

Effect of Temperature 191 

Effect of Barometric Pressure 192 

Effect of Relative Humidity 194 

Effect of Wind Velocity 195 

Relative Effects 197 

Evaporation Formulas 198 

Comparison of Evaporation Formulas 201 

Correction for Size of Pan 204 

Methods of Measurement 205 

Observed Evaporation 206 

Evaporation from Deep Water 214 

Evaporation from Snow and Ice 21«8 



viii CONTENTS 

CHAPTER VI 

Page 

EVAPORATION FROM LAND AREAS 221 

THE RATE OF EVAPORATION 221 

Effect of Temperature 221 

Effect of Relative Humidity 224 

Effect of Vegetation 225 

THE EVAPORATION OPPORTUNITY 226 

Effect of Precipitation 226 

Effect of Interception . 227 

Effect of Percolation 228 

Depth of Percolation and Rate of Return of Moisture by 

Capillarity 231 

Depth of Water-table 235 

Effect of Vegetation 236 

Effect of Drainage 237 

Observed Evaporation Losses from Land Areas 238 

Irrigation Investigations 238 

Relative Evaporation from Land and Water 239 

Effect of Character of Soils 240 

CHAPTER VII 

TRANSPIRATION 242 

Definition 242 

Effect of Temperature 242 

Effect of Humidity 246 

Effect of Wind 246 

Effect of Light 246 

Effect of Soil Moisture 249 

Effect of Character of Vegetation 254 

Effect of Precipitation i 256 

Transpiration Proportional to Dry Matter Produced. . . . . 257 
Amount of Transpiration in Inches Depth over Ground 

Area 259 

CHAPTER VIII 

DEEP SEEPAGE 263 

The Underground Reservoir 263 

Artesian Basins , 264 

Motion of Underground Water 268 

Hazen's Formula , 269 

Slichter's Formula 272 

Comparison of Formulas of Slichter and Hazen 274 

Measurement of Underflow 276 



CONTENTS IX 
CHAPTER IX 

Page 

RUNOFF 279 

Definition 279 

Surface Flow 279 

Effect of Precipitation and Temperature 279 

Effect of Physical Characteristics of Watershed 2S0 

Effect of Drainage of Upland 282 

Effect of Drainage of Swamps 283 

Effect of Lakes and Ponds 283 

Seepage Flow 284 

Effect of Watershed Characteristics 284 

Effect of Character of Precipitation 286 

Changes in Seepage Flow Following Percolation 287 

Depth of Water-table 289 

Effect of Barometric Pressure 289 

Runoff from Typical Watersheds ■ 291 

Watersheds in the Northwest 297 

Watersheds in the East 297 

Southern Watersheds 297 

Western Watersheds 299 

Hydrographs of Daily Discharge 298 

The Flood Flow of Streams 308 

floods due to rainfall 309 

Flood Producing Rains 309 

Intense Rainstorms as Basis for Flood Estimates 310 

Effect of Watershed Area 310 

Effect of Shape and Location of Watershed 311 

Effect of Soil 313 

Effect of Cultural Conditions 313 

Watershed Characteristics Reflected in Floods 313 

Elk River Flood 318 

Root River Flood 319 

Wild Rice River Flood 320 

Scioto River Flood 321 

Ohio River Flood 323 

floods due primarily to snowfall 325 

Accumulation of Snow . . . 325 

Melting of Snow 326 

Crow Wing River Flood 327 

Little Fork River Flood 327 

Effect of temperature and precipitation on winter 

and spring floods 329 

The Ohio River at Pittsburgh 329 

The Upper Mississippi River at St. Paul, Minn 332 



X CONTENTS 

Page 

The Red River of the North at Grand Forks 335 

Mass Curves of Temperatures Above Freezing 335 

FALL FLOODS 341 

FLOOD FLOW FORMULAS 341 

Weight Given to Various Factors by Different Formulas. . 342 

Fuller Formulas 342 

Flood Frequency 345 

Suggested Definition of " Normal " 347 

Data Relating to Some of the Most Severe Floods 348 

summer floods on small watersheds 348 

Cane Creek, N. C, Flood 348 

Heppner, Oregon, Flood 348 

Monterey, Mexico, Flood , 349 

WINTER AND SPRING FLOODS ON LARGE STREAMS 351 

Lower Mississippi River Floods 351 

The Rains Causing These Floods 351 

Flood Damage 353 

Ohio River Floods 353 

Comparative Flood Hydrographs 354 

Flood of 1884 355 

Floods of 1913 355 

Seine River, Paris, Flood 356 

Low Water Flow of Streams 357 

Effect of Precipitation 357 

Effect of Ground-water Supply 358 

Lake and Swamp Storage 358 

Effect of Temperature 360 

Observed Low-water Flows 362 

CHAPTER X 

STEAM-FLOW DATA 367 

Need of Data 367 

How Data are Obtained 367 

CURRENT METER MEASUREMENTS 367 

The Gaging Station 368 

The Meter Section 368 

The Staff Gage 370 

The Hook Gage 370 

The Chain Gage 370 

The Automatic Recording Gage 371 

The Current Meter 375 

Rating the Meter 377 

The Mean Velocity 379 

Making the Measurement 382 



CONTENTS XI 

Page 

The Field and Office Notes 385 

The Discharge Curve 386 

Effect of Ice on Discharge 391 

OTHER METHODS OF MEASURING STREAM FLOW 392 

Float Measurements 392 

Slope Measurements 395 

The Chemical Method 400 

Diaphragm or Traveling Screen 403 

The Pitot Tube 404 

The Venturi Meter ' 406 

Stream-flow Data from Water-power Plants 408 

Where Stream-flow Data are Published 409 

CHAPTER XI 

SUPPLEMENTING STREAM-FLOW DATA 410 

Unreliability of Short-term Means 410 

Comparative Hydrographs 413 

Methods of Computing Runoff , 413 

The " Water Year " 417 

The Author's Evaporation Curve 421 

The Author's Transpiration Curve 424 

synopsis of author's method of computing annual runoff 424 

Computing Annual Yield 426 

Computing Monthly Runoff 428 

CHAPTER XII 

MODIFICATION OF STREAM FLOW BY STORAGE 437 

APPLICABILITY DEPENDENT UPON COST 437 

RESERVOIR SITES 438 

Location ' 438 

Water Supply 438 

Seepage and Evaporation Losses 439 

Spillway Capacity 440 

Dam Site , 441 

Sedimentation of Reservoirs 441 

EFFECTIVENESS OF RESERVOIR STORAGE 441 

Losses in Conveying Channels 441 

Loss Through Temporary Ground-water Storage 443 

Retardation of Seepage Flow 445 

Evaporation Loss in Channels 449 

Other Factors 449 

STORAGE FOR MUNICIPAL PURPOSES * 449 

For Water-supply Purposes 449 

For Improving Sanitary Conditions 450 



Xll CONTENTS 

Page 

STORAGE FOR IRRIGATION 451 

STORAGE FOR LOGGING 452 

STORAGE FOR NAVIGATION 452 

Applicability 452 

The Two Largest Navigation Reservoirs 453 

Effectiveness of Navigation Reservoirs 453 

STORAGE FOR FLOOD PREVENTION 455 

Applicability 455 

Methods 456 

Check Dams 456 

Retarding Basins 458 

Impounding Reservoirs 461 

Control of Mississippi River Floods by Reservoirs 462 

STORAGE FOR POWER 464 

Applicability 464 

Limit of Economical Development 465 

Size of Auxiliary Power Plant 465 

The Mass Curve 466 

Regulation to' Increase Dependable Flow 467 

Regulation to Increase Utilizable Flow ' . 467 

Frequency Curves 468 

Construction of Frequency Curve 470 

CONFLICT OF STORAGE PURPOSES 472 

STORAGE BELOW ORDINARY HIGH-WATER MARK 474 

Ordinary High Water Defined 474 

Storage Limitations 477 

NOTE TO TEACHERS OF HYDROLOGY 477 

INDEX 479 



THE ELEMENTS OP HYDROLOGY 



CHAPTER I 
INTRODUCTION 

Definition of Hydrology. — Briefly stated, hydrology is the 
science which treats of the phenomena of water in all its states; 
of the distribution and occurrence of water in the earth's atmos- 
phere, on the earth's surface, and in the soil and rock strata; 
and of the relation of these phenomena to the life and activities 
of man. 

Present State of Hydrology. — Hydrology is essentially a new 
science. It is founded upon other and better-established sci- 
ences, such as meteorology, geology, agricultural physics and 
chemistry, and botany, besides upon a rapidly growing body of 
physical data peculiar to itself. Our present knowledge of the 
subject is indeed fragmentary and incomplete and is scattered 
throughout the literature of engineering and the other sciences 
mentioned. The complete lack of books on the subject of 
hydrology itself attests the formative character of the science. 
No guide posts but individual judgment indicate the mode of 
treatment to be followed or the field to be embraced in the 
present treatise, and the author freely acknowledges failure to 
attain his ideal and the need for early and thorough revision and 
extension. He trusts, however, that the material and methods 
of analysis presented will be found serviceable in both office and 
class-room. 

Most of the phenomena of hydrology are exceedingly complex, 
and to the casual observer the irregularities and apparent in- 
consistencies are often so great as to make the existence of 
fundamental laws and cause-and-effect relationships seem hope- 
lessly obscure and even completely improbable. Not with- 



2 ELEMENTS OF HYDROLOGY 

standing this seeming confusion, however, the occurrence of all 
natural phenomena will be found based upon law and order, if 
one can only analyze the conditions surrounding these phe- 
nomena and evaluate the varying influences and effects of these 
conditions in each instance. 

In working out the projects of hydraulic engineering, the 
engineer faces a real situation that must be met notwithstand- 
ing the incompleteness of our knowledge of the fundamental 
principles and data of hydrology. However inadequate the 
data, he is forced to draw conclusions and make recommenda- 
tions which often involve considerable expenditures. Moreover, 
the hydraulic engineer cannot safeguard the situation presented 
by inadequate data by introducing the usual factor of safety 
employed in structural work, because if he did nearly all the 
projects of hydraulic engineering would become impracticable. 
Though forced to deal with admittedly incomplete hydrological 
data and uncertain, future occurrences of natural phenomena, 
he is usually limited to factors of safety of about 1.25 to 1.50. 
The structural engineer, on the other hand, dealing with elabo- 
rate test data and material produced according to specifications 
and under supervision, employs factors of safety of 4 to 5. 
Although in most cases human life is not so directly concerned 
in the success of the projects of hydraulic engineering as it is 
in those of structural engineering, the probabilities of financial 
loss are usually greater in the latter field. Since all of these 
projects are, to a greater or less extent, based upon the data and 
principles of hydrology, and since the allowable factor of safety 
or " factor of ignorance " is small, the need for a knowledge of 
hydrology is apparent. 

Application of Hydrology. — Each year sees new improve- 
ments in the structures and machinery involved in the control 
and utilization of water, but the physical data and principles 
upon which the science of hydrology is founded, when once 
fully determined, will ever remain unchanged. These funda- 
mental data and principles find some measure of application in 



INTRODUCTION 3 

nearly every field of engineering and are, indeed, basic to several 
large and important fields. Some of these fields of engineering 
are most intimately concerned with the amount and rate of 
rainfall and the methods of disposing of the excess water which, 
from their viewpoint and within the confines of their field, can 
serve no useful purpose. Such disposal of water may involve 
the prevention of floods and the drainage of agricultural lands 
or of urban communities. Other fields of engineering are con- 
cerned with the conservation of the rainfall which runs off from 
the land or percolates through the soil into the underlying 
strata, and the utilization of this water for domestic and manu- 
facturing purposes, for the irrigation of arid lands, for the de- 
velopment of power, and for the transportation of freight and 
passengers. In the development of cities, engineers are con- 
tinually concerned with the flow of streams. Among their prob- 
lems are the relation of stream flow to water-front improve- 
ments, the disposal of sewage and waste, and the control of 
flood waters. Such, in brief, are a few of the fields of engineer- 
ing to which the science of hydrology is more or less basic. 

Although hydrology has not, heretofore, been generally con- 
sidered a fundamental science, yet it is a fact that the structures 
involved in hydraulic engineering projects far less frequently 
fail to serve their purpose because of fundamental defects in 
structural design than they do because that design is not based 
upon correct hydrological principles and observations. 

Although the specialist in many branches of the engineering 
profession may not always, in the solution of his particular 
problems, require a broad knowledge of the fundamentals of 
hydrology, he will, nevertheless, often derive considerable assist- 
ance from at least a general familiarity with the natural phe- 
nomena that affect the occurrence, distribution, and disposition 
of water on the surface of the earth. 

The development of our country has kept hydraulic engineer- 
ing projects and allied problems involving the principles of 
hydrology almost continually before the public. This has given 



4 ELEMENTS OF HYDROLOGY 

rise to a great clamor for public funds for river improvement, 
reservoir construction, and drainage, and much misinformation 
and misconception regarding the feasibility of such projects has 
been manifested at times. As a member of his community the 
engineer possessed of a knowledge of even the elements of hydrol- 
ogy may wield an important influence in molding public opinion 
regarding the general feasibility of such projects, even though 
the details of the problems involved may be quite outside of his 
own specialty and may require thorough analytical study before 
their solution is finally determined. Through this influence on 
public opinion the engineer may assist not only in conserving a 
natural resource, so far as practicable, but also in conserving 
the tax-payer's money. 

Among the principal controversial subjects of hydrology are 
those concerning the interrelationship of forests, reservoirs, 
drainage and stream flow. The lay mind associates the re- 
moval of forests and the drainage of lands with destructive 
floods, without reference to the cause of floods on different 
streams or the great variation in flood-producing characteris- 
tics of different watersheds. No general deductions of universal 
applicability can be made. Every stream is a problem in itself. 
It follows, therefore, that much detailed observation and study 
are necessary to establish fundamental hydrological principles. 
Observations indicate that forests may both increase and de- 
crease floods; that drainage may both increase and decrease 
stream flow. The conditions under which these effects may 
prevail are discussed later. 

Another subject regarding which much general misinformation 
exists is that of the prevention of floods by storage reservoirs. 
Projects for the impounding of flood-water so as to prevent 
streams from over-flowing their banks and the later utilization 
of this stored water for power development and for increasing 
the depth of navigable streams, appeal to many people as great 
measures of conservation, whereas they are usually good oppor- 
tunities for the waste of public funds. Destructive floods sel- 



INTRODUCTION 5 

dom occur with sufficient frequency to make their water worth 
conserving. Such floods are an evil that must be passed on 
back to the sea as expeditiously and with as little opportunity 
for doing damage as possible. 

Water as a Natural Resource. — The quantity of water with 
which mankind is concerned must always remain substantially 
the same, but its occurrence and its distribution over the surface 
of the earth is continually changing. As an article of use and 
consumption, water is one of those few natural resources the 
supply of which remains substantially undiminished because, 
through the action of natural laws, water is continually per- 
forming an ever-recurring cycle of evaporation, condensation 
and precipitation, ad infinitum. 

The sun's energy vaporizes the water from the surface of the 
earth. The vapor thus formed is lighter than the dry gases of 
the atmosphere, and hence tends to rise. Aided by convection 
currents, the water vapor moves from place to place and upward 
through the air. On rising, it encounters a rarified atmosphere 
and expands. The energy required for the work of expansion 
is drawn from the air itself, resulting in a cooling and ultimate 
condensation of some of the vapor which falls to the earth 
again as rain. The precipitated water then starts on its way 
back to the ocean. Some of it is lost through evaporation and 
some is used by growing plants. The portion flowing over the 
earth's surface and through the rock strata furnishes the water 
for consumption, for power and for transportation. The most 
complete conservation of water can be secured only by its 
fullest utilization, for so long as the sun shines, this natural 
resource is continually being replenished. The intelligent con- 
trol and conservation of water must be based upon the funda- 
mental principles of hydrology. 

The Subject Matter of Hydrology. — The field of hydrology, 
like that of most other sciences, is not sharply demarcated. 
The subject matter is largely drawn from the sciences upon 
which hydrology is founded. In consequence, it is difficult to 



6 ELEMENTS OF HYDROLOGY 

determine, in a book of this kind, what material shall be used 
and what shall be excluded. 

In developing the subject the author has followed what from 
his viewpoint, acquired through about fifteen years of experi- 
ence with the practical problems of hydraulic engineering, 
appeared a logical sequence. Not only the data and considera- 
tions having direct and frequent application have been included, 
but also those facts and principles which are fundamental to a 
more detailed study of hydrology itself. Subject matter which 
did not appear to meet either of these requirements was omitted, 
since this volume is not intended to serve as a comprehensive 
reference book covering every phase of the subject of hydrology. 

Since the sun's heat and the earth's atmosphere are really 
the first causes in the natural phenomena which give rise to the 
problems of hydraulic engineering, these subjects have been 
treated first, in some detail. Solar radiation is the source of 
the heat of the earth that causes evaporation and transpiration 
and the circulation of the air with its vapor content. Unequal 
heating of the earth's surface gives rise to the great air move- 
ments that largely determine our rainfall, our floods, and our 
droughts. These larger atmospheric movements and the sec- 
ondary circulation to which they give rise, together with the 
attendant phenomena, are discussed. This is followed by a 
consideration of water in its various states and their properties, 
with special emphasis on the characteristics and the effects of 
the water vapor of the atmosphere. 

The manner in which water is precipitated out of the air, how 
the precipitation is measured, and the observed rates of precipi- 
tation are treated quite fully. Many tens of thousands of rates 
X)f rainfall are summarized in a manner permitting their true 
significance to be readily grasped, while still preserving the 
original data in sufficient detail to permit of their further analy- 
sis, and the making of independent deductions. The most 
severe rainstorms in different parts of the country are mapped 
for use in determining channel and spillway capacities. Exces- 



INTRODUCTION 7 

sive rates of rainfall are treated in considerable detail and new 
formulas are presented, giving the rates which will be exceeded 
with average frequencies of once in from one to one hundred 
years. 

The subject of evaporation from water surfaces is next treated. 
The factors modifying it are discussed and their relative impor- 
tance is indicated. Some of the best observed data are presented, 
both in tabular and in graphical form, and curves and formulas 
are suggested for practical application. Evaporation from 
water surfaces is substantially continuous at a uniform rate. 
Evaporation from land areas is so irregular as to be almost 
intermittent. The amount of water evaporated from land 
areas depends both upon the rate of evaporation, and upon the 
evaporation opportunity as represented by the available supply 
of moisture, hence the modifying factors are discussed sepa- 
rately. Considerable emphasis is laid upon percolation and capil- 
lary action in different soils and on the effects of vegetation and 
drainage on evaporation losses. This is followed by a discus- 
sion of transpiration, its amount and the factors that modify it, 
viewed from the standpoint of the effect of transpiration upon 
the amount of precipitation that will find its way into the 
streams. The effect of the character of the soil on the amount 
of water available for percolation, transpiration, and evapora- 
tion in different soils is treated, and a new method is presented 
for determining soil moisture in terms of inches of water per 
foot depth of soil under field conditions. 

Consideration of underground water and its rate of motion is 
followed by a discussion of runoff. This represents the residual 
precipitation after evaporation, transpiration, and deep seepage 
losses have been supplied. In dealing with the factors that 
modify runoff the flow of streams is divided into surface flow 
and seepage flow. Typical watersheds are studied with a view 
to bringing out the extent to which watershed characteristics 
are reflected in the hydrographs of streams. Floods due to 
rainfall and snowfall are analyzed to show the cause of floods 



8 ELEMENTS OF HYDROLOGY 

and the relative effects of the various flood-producing charac- 
teristics of different watersheds. 

The factors modifying the low-water flow of streams are next 
discussed, and some observed low-water stream-flow data are 
presented. The fundamental principles and essential facts re- 
garding the various methods of obtaining stream-flow data are 
discussed, but no attempt is made at a comprehensive treatment 
of the subject. For further information the reader is referred 
to Hoyt & Grover's " River Discharge." Methods of supple- 
menting stream-flow data by computing runoff from rainfall 
and other physical data are presented, and finally the modifi- 
cation of stream flow by storage is discussed. The cost of stor- 
age, the factors determining the desirability of reservoir sites, 
losses from reservoirs and the storage of water for municipal 
purposes, for irrigation, logging, navigation, flood prevention 
and power purposes are specifically treated. Mass curves and 
frequency curves are explained, with illustrations of the use of 
typical curves in water-power studies. This is followed by a 
statement of the extent to which the storage of water for the 
various purposes conflict. Finally, reference is made to the 
storage of water below ordinary high-water mark in those por- 
tions of the country where the law of riparian rights holds. 

The arrangement of the subject matter which has been fol- 
lowed appeared logical to the author and he trusts it may also 
be found convenient and conducive to a clear understanding of 
the subject by those who may have occasion to use the book. 



CHAPTER II 

THE ATMOSPHERE: ITS TEMPERATURE, PRESSURE 
AND CIRCULATION 

Use. — The most important direct use of the atmosphere is 
its function in providing plants and animals with the carbon 
dioxide and the oxygen essential to the chemical reactions of 
life, and in preventing the rapid radiation of heat at night 
which would make the earth uninhabitable. Minor, indirect 
uses of the atmosphere are its mechanical power to propel 
wind mills and boats, to distribute seeds and to sustain the 
flight of birds and man. From the viewpoint of hydrology, 
perhaps the most important function of the atmosphere is 
the transportation of water vapor and the absorption of radiant 
energy. 

Composition. — At sea-level elevation the atmosphere is 
composed of substantially 78 per cent of nitrogen, 21 per cent 
of oxygen, .9 per cent of argon, about .03 per cent of carbon 
dioxide, and a greatly varying amount (from less than 1 per 
cent to 5 per cent) of water vapor, in addition to small 
amounts of hydrogen, helium and a few other unimportant 
gases. Above an altitude of about fifty miles the atmos- 
phere appears to be composed primarily of hydrogen, which 
is believed to be continually escaping from the earth's atmos- 
phere into space. The composition of the earth's atmosphere 
is shown graphically in Fig. 1, taken from an article by W. J. 
Humphreys, in the Bulletin of the Mount Weather Observa- 
tory, 1909. 

When the percentage of oxygen in the atmosphere drops 
below 18§ the candle flame dies out. The percentage of carbon 
dioxide is considerably greater over cities than in the country, 

9 



10 



ELEMENTS OF HYDROLOGY 



particularly in calm weather. As high as five to ten times the 
normal proportion of carbon dioxide has been found in crowded 
buildings. A continuous supply of about 2000 cubic feet of 
fresh air per hour is required for each person in order to 
maintain a desirable standard of purity. 



Altitude 



Pressure 



km A Q IQ op 3Q 40 50 qq r0 80 90 10Q mm - '"• 




^ ~-..l -■ f_ . j : ; : 405 

titer \apor- — 5* Carbon bioxidtjS 

I .-..t' M .■ i, . .: .Htgo -i 



10 20 30 40 50 00 70 80 00 100 

Volume Per cent 

Fig. 1. — Distribution of Gases in the Atmosphere (after Humphreys). 



The several gases of the atmosphere exert substantially no 
influence over each other except that the dry gases affect the 
rate of diffusion of water vapor. These gases exist purely 
as a mechanical mixture,, each independent of the others; 



THE ATMOSPHERE 11 

the nitrogen, for example, exists as an atmosphere enveloping 
the earth exactly as if the oxygen and the other gases were not 
present. 

Considering an average dry atmosphere as having a density 
of one, the density of nitrogen is .97, oxygen 1.11, carbon 
dioxide 1.52 and water vapor .62. Nitrogen occurs in measur- 
able quantity to an elevation of about 35 miles above the sur- 
face of the earth, and oxygen to an elevation of 30 miles. 
Carbon dioxide practically disappears at 10 miles, and water 
vapor at 12 miles above the surface of the earth. We know, 
however, from the appearance of meteors and from the phenom- 
enon of diffraction, that the atmosphere, even though rare, 
extends to a very much greater elevation. 

Properties. — The atmosphere has weight, as manifested by 
the height of the column of mercury which it supports in the 
barometric tube and the height of the column of water which 
it supports below the bucket of a pump; it is also highly com- 
pressible, as manifested by the action of the air pump and the 
inflated rubber ball. Each gas of the atmosphere is compressed 
by the weight of the layers of gas above, and consequently 
is denser at sea level than at all points above that elevation. 
If it were not for changes in temperature, the density of the dry 
gases of the atmosphere would be entirely dependent upon the 
volume of each particular gas above the point under consider- 
ation. According to Boyle's law, when the pressure on a given 
volume of gas is doubled, without change in temperature, the 
volume of the gas is halved. When the temperature of a gas 
is changed, the volume of the gas, according to Charles' law, 
increases approximately jb for every increase of one degree 
in temperature, Centigrade. By means of these two laws 
and observed temperatures, the density of the dry gases of 
the atmosphere at any given elevation can be determined. 

The specific heat of the dry gases of the atmosphere, measured 
under the conditions of constant pressure, is .24, and that of 
water vapor is .48 times that of water in the liquid state. 



12 ELEMENTS OF HYDROLOGY 

Amount of Water in Atmosphere. — The amount of water 
vapor present in the atmosphere varies greatly from time to 
time, but the dry gases do not change materially in quantity 
from season to season. During the winter months, in the 
Northwest, no matter how thoroughly saturated the air may 
appear, the total amount of moisture present in the atmosphere 
represents less than half an inch of rain. During the summer 
months, on the other hand, it is not unusual for the total amount 
of moisture in the atmosphere to equal about three inches of 
rain. 

The maximum amount of moisture which could possibly 
be precipitated from the atmosphere at any one time is, nat- 
urally, the total amount of moisture which the atmosphere 
contains. As a matter of fact, however, only that portion of 
the moisture which can be precipitated as the result of the 
change in temperature accompanying the rise of the water 
vapor to the upper cloud level can fall as rain. This amount, 
uniformly distributed, represents about one-tenth inch of rain- 
fall in December and six-tenths inch in June. 

The only reason why, over a restricted area, larger amounts 
of precipitation than those above mentioned ever occur, is 
because of the fact that part of the rainfall is derived from 
moisture present in the atmosphere over adjoining land or 
water areas which is brought in from all sides, by the wind, to 
the restricted low-pressure area under which the maximum 
precipitation occurs. Heavy rainfall can occur only over small 
areas. General, well-distributed rains are nowhere excessive. 
This phase of the subject is discussed in detail in a later chapter. 

Distribution of Water Vapor. — The water vapor is not 
distributed through the atmosphere in accordance with the 
laws of Boyle and Charles because of the fact that under 
the ordinary conditions of the atmosphere it exists as a 
nearly saturated vapor, which, with relatively small change 
in temperature and pressure, will be condensed and partly 
precipitated. Under natural conditions the other gases of the 



THE ATMOSPHERE 13 

atmosphere never meet with sufficient increase in pressure, and 
decrease in temperature to reach the liquid or the solid state. 
Hence, the distribution of water vapor through the atmosphere 
is determined primarily by temperature. 

As the amount of water vapor present in the atmosphere is 
dependent mainly upon its temperature, the subject of temper- 
ature will be considered before the distribution of water vapor 
in the atmosphere is further discussed. It may be remarked at 
this point, however, that about half of the total moisture pres- 
ent in the atmosphere is found below an elevation of about 
6000 feet, and less than one tenth of it occurs above an elevation 
of 20,000 feet. 

Temperature 

Source of All Heat. — The temperatures with which the 
science of hydrology is primarily concerned are the temperatures 
of the air, the water and the soil. Changes in temperature 
merely represent changes in the great velocity with which the 
molecules constituting the various gases, or liquids, or solids are 
moving back and forth over their minute paths. The ultimate 
cause of all changes in temperature is the sun. Radiant energy 
reaches us from the sun in the form of waves having various 
lengths, but even the longest are inconceivably short. These 
waves travel at the rate of 186,000 miles per second. A por- 
tion of the radiant energy from the sun is absorbed by the 
atmosphere during the passage of the sun's rays through it. 
The radiant energy so absorbed increases the rate of vibration 
of the molecules of the gases of the atmosphere — that is, 
increases its temperature. The portion of the energy which 
reaches the earth's surface accelerates the motion of the mole- 
cules of water, soil and other material, and hence raises the 
temperature of those objects. The surface of the earth, in turn, 
radiates heat outward, thus again increasing the temperature 
of the air above it. 

The heat absorbed by water areas of given depth for a given 



14 ELEMENTS OF HYDROLOGY 

rise in temperature is about four times the amount absorbed 
by equal land areas and to equal depths for the same rise in 
temperature. Various soils also exhibit different heat absorb- 
ing and reflecting properties. Sand, for example, will absorb 
about twice as much heat as humus and about one and a half 
times as much as clay. On the other hand, during the night, 
humus will quickly radiate into the atmosphere even the little 
heat absorbed during the day, making highly vegetable soils 
essentially cold soils, and sandy soils essentially warm ones. 

Effect of Water Vapor on Solar Radiation. — The water 
vapor in the atmosphere virtually governs the portion of the 
solar energy which is absorbed during its passage to the earth. 
This is due to the great changes in the water vapor content 
of the atmosphere and its high specific heat. Just twice as 
much heat energy is required to raise a given weight of water 
vapor one degree in temperature, as is required to raise the 
same weight of dry air an equal amount. To raise the tem- 
perature of liquid water one degree requires substantially twice 
the amount of heat energy required to raise the same weight 
of water vapor an equal amount. 

The presence of water vapor in the atmosphere also mate- 
rially influences the rate at which heat is radiated back into 
space by the earth during the night time. Clear nights are rela- 
tively cold nights; cloudy nights are invariably warmer than 
they would be if the moisture in the atmosphere did not prevent 
the rapid radiation of heat from the earth's surface. 

The amount of solar radiation or insolation received at the 
surface of the earth varies greatly with the altitude of the sun, 
mainly because of the difference in the thickness of the layer 
of atmosphere through which the rays of the sun must travel. 
At sunrise, for example, the sun's rays travel through approxi- 
mately 35 times the thickness of atmosphere traveled through 
at noon on a summer day. For this reason the amount of 
solar radiation received by the surface of the earth varies greatly 
with altitude, and also with latitude. 



THE ATMOSPHERE 15 

It has also been observed that extensive forest fires and vol- 
canic eruptions, through the dust which is emitted into the 
atmosphere, substantially reduce, for such considerable periods 
of time as a year, even, the amount of solar radiation received 
in some localities. 

Measurement of Solar Radiation. — The little glass globe 
and its revolving black and white vanes, frequently seen in 
opticians' windows, is a familiar object to all. This principle 
of the absorption of heat by black objects and its reflection 
by white objects is utilized in the construction of pyrheliometers, 
— instruments used for the measurement of solar radiation. 
Pyrheliometers consist, essentially, of black and bright bulb 
thermometers placed in a vacuum. In general, the black ther- 
mometer registers from 30 to 60 degrees higher than the bright 
thermometer. On mountain tops in the bright sunshine, the 
temperature of the black bulb thermometer has reached over 
230 degrees. The solar radiation temperatures in the Polar 
regions are surprisingly high, largely on account of the absence 
of water vapor. It has been found, for example, that in the 
Arctic region, with the altitude of the sun at only about 30 
degrees, the mean black bulb temperature in June was only about 
14 degrees, Fahrenheit, less than that at Madras, with an 
almost vertical sun. 

Amount of Solar Radiation Received. — The amount of 
solar radiation received on a clear summer day on each square 
yard of the earth's surface represents about 1.2 horsepower. 
Fig. 2, reproduced from the August, 1914, Monthly Weather 
Review, is a graph of the solar radiation received at Mount 
Weather Observatory, Virginia, Latitude 39° 4' N., on May 
8, 1913. Two curves are shown in this diagram. The upper 
curve shows the total amount of solar radiation received from 
hour to hour, and the lower curve shows the amount of sky 
radiation received at the same time. By sky radiation is meant 
the energy radiated from the sky as recorded by the pyrheliom- 
eter when completely shielded from the direct rays of the sun. 



16 



ELEMENTS OF HYDROLOGY 



The amount of solar radiation received at the surface of the 
earth during the varying seasons and in various localities is 
of tremendous importance in the science of hydrology because 





j ^:: *v t 


I Total Radiation— k/' fV 


1 1 y V II 


± _,?£::: :;:: ~:\ ± 


At - 1\ X 




J__+_ - _..:.. I ^ |_ 


4, - ., ^mgffli- -il Ul 


.. <i— - rt ^^pfctscsrr 


J^. tr l . . IM^ 



10 11 Noon 1 

True Solar Time 

Fig. 2. — Daily Variation in Solar Radiation, Mount Weather, Va., 

May 8, 1913. 

of its effect on the cycle of evaporation, condensation and 
precipitation of water, and on the growth of plants. 
„„„ j fmamjjasond The upper curve of Fig. 3, 

prepared from data published 
in the Monthly Weather Re- 
view, shows the average total 
daily amount of solar radia- 
tion received during the dif- 
ferent months of the year, at 
the Government Observatory, 
at Mount Weather, Virginia, 
during 1912, 1913 and 1914. 
The lower curves of the same 
Figure show the maximum 
daily rate of radiation at 
Mount Weather for each 

i a s o n d montn of the y ear > based on 
Fig. 3. — Annual Variation in Solar observations taken since 1907. 
Radiation at Mount Weather, Va., The solar radiation received 

Latitude 39° 4' N. , A - , , 

on a surface perpendicular to 

the rays of light, and on a horizontal surface are both shown. 

It is worthy of note that the maximum radiation received on 



































































































^ 








A 
I) 


ver 

aily 


it," 
Ita.i 


r.jtu 

iati< 


I 
n 










































/On 


Normal S 


irfair 


■ 


















































On 






Surf 


oe 




































































Dai 


Maxi 
y Rate 


nun 
>f K 


idia 


ion 































THE ATMOSPHERE 



17 




40° 60° 

Latitude 



Fig. 4. — Relative Total Annual So- 
lar Radiation Reaching Earth. 



a normal surface is substantially the same in December as in 

June. The intensity of the sun's rays on a clear December 

morning is a matter of common observation. 

Fig. 4, prepared from data given by Moore,* shows the rela- 
tive total annual amount of solar radiation received at the outer 

atmosphere in various latitudes, 

and the portion which reaches 

the earth's surface, together 

with the portion absorbed by 

the earth's atmosphere. 

It will be noted that while 

the amount of heat and light 

received from the sun at the 

outer atmosphere is only about 

2\ times as great at the equator 

as at the poles, the amount 

actually reaching the earth's surface in the equatorial regions is 

6 times as great. 

Fig. 5 shows the relative total monthly radiation as calculated 

by Angot to reach the earth at the various latitudes, assuming 

that, on an average, 40 per cent 
of the daily radiation is ab- 
sorbed. As a matter of fact 
considerably more is absorbed, 
but on account of the varying 
degree of cloudiness the true 
total average absorption by the 
atmosphere is difficult of de- 
termination. 

The reason for the rapid 
growth of all vegetation during 

the short summers of the middle latitudes is forcibly brought to 

one's attention by the preceding diagrams. The amount of 

water used by plants is, in general, proportional to their growth. 
* Moore, W. L., Descriptive Meteorology. 





J 


F 


M 


A 


M 


J 


J 


A 


s 





N 


D 






..» 


Lat 


tude 


o£C 


entral W 


imp 


iota 


(45°) 


























UE 


luat 


>r 




o 
a 
























"0 

a 
K 


























_2 



m 


































/ A 


Noi 
Poll 


th 







































Fig. 5. — Relative Monthly Mean So- 
lar Radiation Reaching Earth. 



18 



ELEMENTS OF HYDROLOGY 



The water used by plants is not available as a runoff; conse- 
quently solar radiation becomes a factor influencing stream 
flow. This phase of the subject will be further discussed in a 
later chapter. 

The following table * shows the aggregate number of hours 
of daylight, twilight and night at the equator and at the poles. 



At the equator 


At the poles 


4407 hours dav 
864 " twilight 
3495 " night 


4450 hours dav 
2403 " twilight 
1913 " night 



It has been calculated that the amount of solar heat received 
by the earth in a year is sufficient to melt a layer of ice 141 
feet thick, or to evaporate a layer of water nearly 18 feet thick, 
covering the whole earth's surface. If it were not for the pres- 
ence of the atmosphere, however, and its effect in preventing 
rapid radiation at night, the temperature of the surface of the 
earth, in spite of the large amount of heat received from the 
sun during the daytime, would drop to about 325 degrees 
below zero, Fahrenheit. 

In perfectly clear weather, with the sun directly overhead, 
about 75 per cent of the solar radiation reaches the earth's 
surface, the remaining 25 per cent being absorbed by the 
atmosphere. The heat rays are much more readily absorbed 
by the atmosphere than the light rays, so that when the sun 
is near the horizon we may receive considerable light but little 
heat. In latitude 45 degrees a little over half of the solar 
radiation is absorbed by the air. According to Abbot, con- 
sidering the earth as a whole, 76 per cent is absorbed. 

Refraction. — There is a period each day for an hour or more 
before sunset until sometime after, when the heat received 
by the earth from the sun is equal to the amount radiated 
by the earth into space. A similar though shorter period 

* Waldo, Frank, Elementary Meteorology. 



THE ATMOSPHERE 19 

occurs in the morning. This is the period best suited for 
astronomical observations and accurate survey work. During 
these periods objects appear steady in the object glass of the 
telescope, as is well known to all surveyors. The unsteadiness 
of objects during the daylight hours is caused mainly by the 
unequal refraction of light. Snow always has a particularly 
bad effect. 

Temperature Data. — Temperature data for the United 
States, which are of great service in the field of hydrology, 
are collected and published by the Weather Bureau of the Depart- 
ment of Agriculture. Observations are made at a total of 
nearly 6000 stations. Only about 200 of these, however, are 
paid observer stations, equipped with a full set of instruments 
and at which all the principal phenomena relating to the weather 
are observed. About 4200 stations are known as "cooperative 
observer stations," at which the observer receives no compensa- 
tion except in the form of certain publications of the Weather 
Bureau. The remaining stations are special paid stations 
at which only certain observations are made relating to crop 
conditions, river stages, etc. The cooperative observers re- 
cord only rainfall and maximum and minimum temperature, 
and make notes regarding the general condition of wind and 
weather, early and late frosts, appearance of aurora, etc. Fig. 6 
shows a typical cooperative observer station. The thermome- 
ters are located in the shelter and the rain gage is at the right. 

Thermometers. — The maximum thermometer used by the 
Weather Bureau consists of a long graduated mercury tube 
and bulb. Just above the bulb the tube is constricted so 
that when the mercury contracts after having reached its 
maximum height, the column breaks at the constricted section, 
leaving the upper portion registering the maximum temperature 
within a few tenths of a degree. When the thermometer is 
subject to slight jarring or vibration, the column breaks 
sooner, and hence registers more accurately, than when it is 
kept perfectly quiet. 



20 



ELEMENTS OF HYDROLOGY 




Fig. 6. — Typical Cooperative Observer Station. 



THE ATMOSPHERE 



21 



. The minimum thermometer is filled with alcohol. In the 
tube of the thermometer an index is floated which, as the alco- 
hol contracts, is carried downward by the surface tension of 
the liquid. When the alcohol expands after having reached its 
minimum temperature, the liquid does not carry the index 
up with it. The accuracy of such a thermometer is about 
half a degree. Both maximum and minimum thermometers 
are kept in a nearly horizontal position. 

Where a continuous record of temperature is desired, a re- 
cording thermometer, such as the ''Thermograph" of Fig. 7, 
is used. 




Fig. 7. — Thermograph. 



Daily Mean. — The maximum air temperature usually 
occurs soon after noonday, and the minimum air temperature 
usually occurs just before sunrise. It has been found that. 
on an average, the mean of the maximum and the minimum 
temperatures in any 24-hour period is about .4 to .5 degrees 
less than the true mean daily temperature. The mean of the 
9 a.m. and the 9 p.m. readings is also about half a degree 
low. The mean of the 8 a.m. and 8 p.m. readings is 



22 



ELEMENTS OF HYDROLOGY 



a.m. m: 

i 6 8 10 12 



P.M. 

4 6 8 10 12 



about .2 or .3 of a degree low. One fourth of the sum of the 
7 a.m. plus the 2 p.m. plus twice the 9 p.m. temperatures is 
almost exactly equal to the true mean daily temperature. A 
single day's observations, of course, may depart considerably 

from the above expressed 
mean relationship. 

Daily Variation. — The 
daily temperature changes 
on the earth's surface vary 
greatly with latitude. In- 
asmuch as the sun shines 
for 12 hours at the equator 
and then disappears for 12 
hours, it is evident that 
the daily changes in tem- 




Fig 



Mean Daily Variation in Tem- 



perature measured from Maximum. 



J F M A M j j 



S O N D 



o20 



£40 

a 
> 



perature, other conditions remaining the same, must be greater 
at the equator than in the regions toward the poles where 
the sun may shine continuously for days, weeks or even 
months at a time. This is 
illustrated by Fig. 8, which 
shows the mean daily varia- 
tion in temperature at typi- 
cal continental stations in 
various latitudes. 

Annual Variation. — The 
variations in annual temper- 
ature are opposite, in rela- 
tive magnitude, to the varia- 
tions in daily temperature. 
As the sun shines 12 hours a 
day, each day in the year, at the equator, and shines continu- 
ously for days and even months in the polar regions, and then 
disappears from those regions altogether for an equally long 
time, it is apparent that the annual fluctuations in temperature, 
other conditions remaining the same, must be far greater in 



GO 











/' 






V 


\ 










Sa 
La 


ita 

.35° 


^7* 


7 








\\ 


\ 

\ 










4 

/ 


/ 




I 


St.] 

.at. 


'aul 
1 58 




i \ 
\ 


\ 
\ 






S 


/ 


1 












\ S 


\ 


V 






/ 

/ 

f 
















\ 

> 




s 


/ 




































Ft 
Li 


.Cm 
it. 8 


ger 
°42'- 































Fig. 9. — Mean Annual Variation in Tem- 
perature measured from Maximum. 



THE ATMOSPHERE 



23 



111 




















30 






































20 






































10 











































" 

















40° 60° 

Latitude 



80° 90 



the polar regions then at the equator. This fact is well illus- 
trated by Fig. 9. 

The mean difference between July and January temperatures 
in various latitudes north of 
the equator, according to 
Hann,* is shown in Fig. 10. 

Periodic Variation. — In 
addition to the daily and 
hourly changes in tempera- 
ture and the more or less 
irregular changes accompany- 
ing daily changes in weather, 
long-term temperature obser- 
vations indicate a fluctuation Fig. 10. — Mean Difference between July 

, i i j. and January Temperatures in Various 

in the mean annual tempera- T ..■. , 

^ Latitudes. 

ture over periods of varying 

length, with indications of 35-year cycles and minor periodic 
variations occurring in 11 -year and 3f-year intervals in syn- 
chronism with sun spots and solar prominences. 

Extremes of Temperature. — The greatest temperature 
changes occur in Siberia. According to Hann, the lowest tem- 
perature ever observed is —90.4°. At Havre, Montana, there 
has been an extreme range of from —55° to +108°. At Poplar 
River, Montana, a minimum of —63° has been recorded, and at 
Mammoth Tank, California, a maximum of 128°. 

Maps of maximum and minimum recorded temperatures in 
the United States are shown in Figs. 11 and 12. 

Variation with Altitude. — Besides these changes in temper- 
ature with the changing seasons, the science of hydrology is 
intimately concerned with the variations in the temperature 
of the atmosphere with altitude. The actual observed decrease 
in temperature is about one degree, Fahrenheit, for every 300 
feet increase in latitude. This reduction in temperature with 
altitude does not continue indefinitely, however, as is well illus- 
* Hann, Dr. Julius, Lehrbuch der Meteorologie. 



24 



ELEMENTS OF HYDROLOGY 




THE ATMOSPHERE 



25 




26 



ELEMENTS OF HYDROLOGY 



trated by Fig. 13, reproduced from Sir John Moore's "Meteor- 
ology." This figure is a graph of the reduction in temperature 
recorded by " sounding balloons " sent up to high altitudes. 




240 350 260 

Temperature Absolute 

Fig. 13. — Relation between Temperature and Altitude as determined by 
" Ballons-Sondes " (after Moore). 

After an elevation of about seven miles is reached, it will be 
noted, there is no further reduction in temperature. Below 
that elevation the average slope of the lines in Fig. 13 indi- 



THE ATMOSPHERE 27 

cates an average reduction in temperature of one degree in 
300 feet, as above stated. This reduction in temperature has 
a tremendous influence on the condensation and precipita- 
tion of water. Water vapor moving upward a given distance 
will encounter a very much greater change in temperature 
than it could ever encounter in moving the same distance 
horizontally along the surface of the earth. This phase of the 
subject will be further , discussed in connection with rainfall. 
Extending Short-term Records. — Inasmuch as observations 
of temperature have been made for varying periods of time at 
the different Weather Bureau stations in the United States, 
it is frequently necessary to supplement and extend short- 
term records for the purpose of securing a satisfactory com- 
parison between prevailing temperatures at two given stations. 
A similar need for the extension of short-term records exists 
when attempting to prepare maps showing lines of equal tem- 
perature, or isotherms. Under such circumstances, instead of 
using the mean of a varying number of years' records, it is 
best to compare the mean temperature at the short-term station 
with the mean temperature for the same period of years at 
the nearest, similarly located, long-term station, and then to 
assume that the same relationship would exist between the 
long-term means at these two stations. In this way the effect 
of periodic changes in temperature is eliminated, as the short- 
term mean might cover a series of either warm or cold years. 

Pressure of the Atmosphere 

Amount and Variation with Altitude. — The force of gravity 
acting on the molecules of the various gases of the air causes 
the atmosphere to exert a pressure on the surface of the earth, 
averaging substantially 14.7 pounds per square inch at sea level. 
This pressure is equal to the pressure of a water column 33.8 
feet high, or a mercury column 29.9 inches high. The usual 
way of measuring barometric pressure is by means of a column 
of mercury in a mercurial barometer, although the aneroid 



28 



ELEMENTS OF HYDROLOGY 



barometer serves a similar purpose. The pressure of the atmos- 
phere diminishes with altitude approximately in accordance 
with the following simple equation, which serves every ordinary 
engineering purpose. 



Log barometric pres. in ins. mercury = 1.47712 — 



altitude in ft. 
64,000 



Temperature - Degrees F. 
-280 -260 -2J0 -220 -200 -180 -160 -140 -120 -100 -80 -60 -40 -2^ 20 40 60 80 
Absolute Temperature - Degrees C. 
w 100 120 140 160 180 200 220 240 260 280 300 


CO t- 

<5 O 

« a 

J0— 16,000 

9 

14,000 

8— 
12,000 

7— 

10,000 
©6 — 

3 
















1 


































» 












































V- 


















4— 












\fc 




^% 


'% 




3— 

4000 






















2— 






X 
















1 — 

0— 


























2 


4 





10 


20 





100 


200 



Actual Vapor Pressure - mm. Hg. 
6 8 10 12 14 

Relative Humidity - Per cent 
30 40 50 60 70 

Barometric Pressure - mm. Hg. 
300 400 500 600 700 



16 


18 


20 


80 


90 


100 


800 


900 


1000 



Fig. 14. — Variation of Meteorological Elements with Altitude. 

Fig. 14 is a typical graph of the reduction in barometric 
pressure, temperature, relative humidity and water vapor con- 
tent of the atmosphere, with increase in, altitude, over the 
Atlantic Ocean in middle latitude in September, 1907. This 
figure is based on data observed by the U. S. Weather Bureau 
by means of "sounding balloons." 



THE ATMOSPHERE 



29 



Table 1 gives the pressure of the atmosphere at various 
elevations above and below sea level, according to several 
different measures having common application. 





TABLE 


1. — ATMOSPHERIC PRESSURE 














Temperature 


Inches of 
mercury 


Pounds per 
square inch 


Atmospheres 


Feet of 
water 


Elevation in 
feet 


of boiling point 
of water, 
degrees F. 


31 


15.2 


1.03 


35.1 


-890 


213.9 


30 


14.7 


1.00 


34.0 





212.2 


29 


14.2 


0.97 


32.9 


920 


210.4 


28 


13.7 


0.93 


31.7 


1,880 


208.7 


27 


13.2 


0.90 


30.6 


2,870 


206.9 


26 


12.7 . 


0.86 


29.5 


3,900 


205.0 


25 


12.2 


0.83 


28.3 


4,970 


203.1 


24 


11.7 


0.80 


27.2 


6.080 


201.1 


23 


11.3 


0.76 


26.1 


7,240 


199.0 


22 


10.8 


0.72 


24.9 


8,455 


196.9 


21 


10.3 


0.69 


23.8 


9,720 


194.7 


20 


9.8 


0.67 


22.7 


11,050 


192.4 



High- and Low-pressure Areas. — Local heating of portions of 
the earth's surface results in an expansion of the atmosphere 
upward, causing some of the air in the upper layers to flow 
outward and away from the heated area, with a consequent 
reduction in barometric pressure over that area. During the 
summer months there is a permanent region of low barometric 
pressure over northwestern United States and Western Canada, 
and a region of high pressure over the Pacific Ocean to the west. 
During the winter months the condition is reversed. These 
permanent regions of high- and low-pressure result from varia- 
tions in temperature, the land area being warmer in summer and 
cooler in winter. Usually, as soon as the difference in pressure 
between a low- and a high-pressure area becomes greater than 
about one half an inch of mercury, a well-defined easterly 
cyclonic movement sets in. While these storm centers travel 
over different routes, most of them find their way out through 
the St. Lawrence valley. 

Daily Variation in Pressure. — Aside from the large and 
irregular variations due to the passage of storms, the baromet- 



30 



ELEMENTS OF HYDROLOGY 



ric pressure has been found to vary in semi-diurnal waves, 
as shown in Fig. 15 based on data given by Hann * reaching 
the principal maximum at about 10 o'clock in the forenoon, and 
the principal minimum at about 4 o'clock in the afternoon. 
The secondary maximum occurs shortly before midnight, and 

A.M. M. P.M. 

pjjf 12 2 4 6 8 10 12 '3^4 6 8 10 12 

1 + 100 



-100 









1 






1 












• ■- k 
















/ 


' \ 








,. 


Lat'itud 


rr°3o^" 












J-^X 






f 






Latitude 43f 30< 


/ » \ 






/ , 


*■•" 










/V'l ^> 


■V 


s 


fe 










J 


^^, 




V 


t v— 




7T 










^i 










/ 


Latitude 59° 52AN 




.' 


/ 
















\ 


^-.^ 


/I 






\ 


^ 








\ 




1 






















1 
























/ 






















y 









Fig. 15. — Mean Daily Variation in Barometric Pressure. 

the secondary minimum at about 4 o'clock in the morning. 
It will be noted that the daily variation in pressure decreases 
rapidly from the equator to the poles. 

Fig. 16, also based on data given by Hann, shows the effect 
of clouds on the daily variation in barometric pressure. 









A.M. M. 

S 10 R 


. 4 


P.M. 



> 10 12 


£ 








\ 












a 






















s 








s'\ - 


^'Bricrht Day 








u . 


s 




/ 




\ 


1 








~* 


•2 K o 


-IS 








V 


i 










,. — 






X 


~~P r 












'' 




• 2 I 






-^FcioJidv' 


>ay 














rt 






i J: 






\ 










3 


















> 




1 















Fig. 16. — Effect of Clouds on Daily Variation in Barometric Pressure. 

Synchronism of Various Phenomena. — It is an interesting 
fact, shown by Figs. 17 and 18, f that a number of solar and ter- 
restrial phenomena show a similar variation. The interdepend- 
ence of these phenomena is clearly shown by their synchronism. 

The temperature variation at the surface of the earth shows 

a single diurnal wave. Above an altitude of about 400 meters, 

however, the temperature change assumes the semi-diurnal 

* Hann, Dr. Julius, Lehrbuch der Meteorologie. 

t Bigelow, Frank H., Atmospheric Circulation and Radiation, 1915. 



THE ATMOSPHERE 



31 



wave form as shown in Fig. 19.* Above an elevation of about 
2500 meters or one and one half miles both temperature and 
pressure remain substantially constant throughout the day. 
This fact is well shown by Figs. 19 and 20.* 



0a.m. 2 4 6 8 10 0p.m. 2 4 G 8 10 


Cordoba 


C 

AT +i.o 

Temperature 0.0 




























































































\ 






^ 


















\ 




500 meter level —1.0 

m.m. 

AB -0.50 

Pressure o.OO 






















v 




i00-1000 meters 
Cordoba 








































/■ 






















/ 
























/ 












+ 0.50 

, m.m. 

A e -1.00 

Vapor pressure 0.00 


_^/" 
























Surface 
Sal ton Sea 






























































/ 
























/ 










+1.00 

V 

AV -25 
Electric Potential 0.0 












^y 














California 

Grenwich. 
Paris 








































s- 


























































+ 25 

a' 

+ 0.10 
Electric 
























/ 


Potsdam 

Potsdam 














































































s 








/ 












Dissipation —0.10 








\^ 


















Daroca 



















































Fig. 17. — Synchronism of Various Phenomena (after Bigelow) . 

Greatly conflicting theories have been advanced regarding 
the cause of these semi-diurnal pressure waves. One explanation 
given for the occurrence of the early morning minimum is that 
it results from the formation of dew, the precipitation of some 
of the moisture in the air producing a reduction in barometric 
pressure. The latest explanation is that given by Professor 
Bigelow about as follows: The fundamental cause of the daily 
variation of barometric pressure is the diurnal convection. The 
rising air cools by expansion, and the falling air heats by com- 
pression, the former producing the afternoon wave and the latter 
the night wave to within 400 meters of the surface. At this 
elevation the more rapid cooling of the ground during the night 
makes itself felt, and there is radiation from the descending air 
to the ground. 

* Bigelow, Frank H., Atmospheric Circulation and Radiation, 1915. 



32 



ELEMENTS OF HYDROLOGY 



1875 1880 1885- 1890 1895 1900 1905 






v^"^v 


y — *v 


/ \ 


/ % 


Sun Spots f~ V 


7 V 


11.1 year / y 


' \ z 


V z \., 


z s 7 


a»^ ^X- -C\- -£X- 


^v / 


Qh . M 4"V 7 -.4 P 


^ 7 r- 7^ _ 7 


Short period / \ / 1 1 H 


H E -4 4 4 


3.-0 J-eai ' 1 ' V/ _lj l 


4 -i vl X " t 


1 \l <* * v 


7 /aj^7 O 47 ^ 


+ 400 ^ -/\- 




+ 200 -/ u- EX 


-j i- -4 X ^t- 


Solar "8 7s T L f-T 


A/-S /A /' V - 


Prominences —200/ \ / \/J 1 \ 


4 \7 ^ V \7 


mm \t "^ I! 4 




-0.50 _ _ii. '_ 




Aro-onfim. - - 26 74 X -I /1\ ^ 


k A A-AV 


Earomctrt °- 00 P '1 P I \ 


1 L 1 L 4 liJl^ 


Pressure + - 26 J L4 ' / U V 


I I r t t ^-\^r 




' \7 47 




r \ -/V -T- 


+o!26 71 74 ^ rv 


-a, _i J 41 'X 


Temperature 0.00 / ■ J \ / 1 \ 


2 V 4 P7P 


Centigrade -0.26 J \j J_ \ 


t \ 1 ^ P7 N 


\J ^ ~L 


44 t-i 




44 


*M0 2vIi ^ ^2v -Ti- 


■4"PZV\ P 


Excess o.o r t r\ r n r 


h'V-/"^ ' 4 3 4 


Precipitation .joq U/ \ / \ / 1 


3 t-7 W 4 7 


:: II i 


Z it ^ / v.r 








4v- ^ O -/'V 




P 4 ^ -/ r-7 S 


Fahrenheit -0.5,' \ / \ , i/ \ 


j 4 / Li t' 


-1,0 7 ^, T ^^ 


^ ^J 4Z 






1 




+i5.o t 7r 




-U2.0 _J_ 1 




+ 9-0 I 1 




+ 6-0 E . ' _^y 


^4 ^^ 




■ -f^ - ft -i 


p.v,p SS ' o.o J J , 7"! 


-^7\- -4 - tt-A 4 


Precipitation —3.0^ E -Y4 ' i 


■ X 4 - t J^l4 4 


-6.o ^ ^^ r_/ . 


W ^ tj IT 


-9.0 ,J E7 


^^ -^ hf 


-12.0 tj IT 


\r 


-15.0 V/J \T 




J_ 





Fig. 18. — Variations in Solar and Terrestrial Phenomena (after Bigelow) . 



THE ATMOSPHERE 



33 




Fig. 19. — Diurnal Temperature Wave changing to Semi-diurnal Wave at 
Altitude of about 400 meters, and vanishing at Altitude of about 2500 
meters (after Bigelow). 




Fig. 20. — Semi-diurnal Pressure Wave vanishing at Altitude of about 2500 
meters (after Bigelow). 



34 ELEMENTS OF HYDROLOGY 

Circulation of the Atmosphere 

Wind Pressure. — Winds are important phenomena to the 
engineer ; both from the viewpoint of the pressures produced on 
structures and of the excessive rates of rainfall made possible 
only through the circulation of the atmosphere. 

Until the failure of the great steel bridge across the River Tay, 
in England, on December 28, 1879, the subject of wind stresses 
in structures had received little attention. Today the engineer 
who neglected at least to consider the possible effect of wind 
pressures in the design of a structure would be remiss in his duty. 
The values to assume for wind pressures and the determination 
of the resulting stresses, however, is no simple matter. 

The wind pressure, in pounds per square foot, on a normal 
surface, is approximately equal to .004 times the square of the 
wind velocity in miles per hour, times the barometric pressure 
in inches mercury, divided by 30. A pressure of 50 lb. per 
square foot, for example, under normal barometric pressure, 
represents a wind velocity of about 112 miles per hour; 30 lb. 
per square foot represents a wind velocity of about 86 miles per 
hour. These wind pressures represent the highest pressures to 
be expected during " straight blows." " Twisters " — torna- 
does — produce wind pressures against which it is impracticable 
to design. Wind velocities in tornadoes have been estimated 
at 300 to 500 miles per hour, with wind pressures of about 300 
lb. per square foot. The sudden reductions in barometric 
pressure in a tornado cause great outward pressures on closed 
buildings, resulting in the blowing open of doors and windows, 
and other manifestations of explosive action. 

The following table by Moore * gives the common name and 
significant facts regarding various wind velocities: 

* Moore, W. L., Descriptive Meteorology, 1911. 



THE ATMOSPHERE 



35 



Name 


Veiocit 
per 


v, miles 
hour 


Apparent effect 


Calm 







No visible horizontal motion to inanimate 




matter. 


Light 


1 to 


2 


Causes smoke to move from the vertical. 


Gentle 


3 


5 


Moves leaves of trees. 


Fresh 


6 


14 


Moves small branches of trees and blows up 

dust. 


Brisk 


15 


24 


Good sailing breeze and makes whitecaps. 


High 


25 


39 


Swavs trees and breaks small branches. 


Gale 


40 


59 


Dangerous for sailing vessels. 


Storm 


60 


79 


Prostrates exposed trees and frail houses. 


Hurricane. , . . 


80 or 


more 


Prostrates everything. 



Cause of Winds. — The fundamental cause of the circulation 
of the atmosphere is the unequal heating of portions of the 
earth's surface. As the sun travels to the north of the equator 
during our summer, and again south during our winter, there is a 
shifting of the thermal equator. This and other factors result 
in some irregularities in the otherwise rather permanent and con- 
tinual interchange of air between the warm equatorial regions 
and the cold polar regions. The land areas heat and cool more 
rapidly than the water areas in the same latitude. Differences 
in temperature between the equator and the poles result in north 
and south winds. Differences in temperature between the large 
land and water areas result in east and west winds. These 
larger, general wind movements are modified by the rotation of 
the earth, giving rise to certain fairly well-defined wind zones. 

Wind Zones. — In the tropics there is a region of calms or 
doldrums, where the air movement is upward, resulting in almost 
daily heavy rainfall. On each side of this belt of equatorial 
calms there is a region in which the air moves toward the equator. 
Through the rotation of the earth, these air currents are deflected 
from true north and south winds into a westerly direction, and 
are known as the northeast trade winds in the northern hem- 
isphere and the southeast trade winds in the southern hemisphere. 
In the upper air the currents, known as the counter, return or 
anti-trade winds, are in the opposite direction. At approxi- 
mately latitude 30 degrees, north and south, the air currents are 



36 



ELEMENTS OF HYDROLOGY 






0-f-# 




I 



downward, resulting in low humidity and light rainfall. These 
belts are known as the calms of Cancer and of Capricorn. 

- From latitudes 30 degrees toward the poles, covering most of 
the temperate and more densely populated portions of the earth's 
surface, there is the region of the prevailing westerlies, domi- 
nated by areas of low and high barometric pressure resulting 
from the unequal heating of the land and water masses. These 
low- and high-pressure areas follow each other across the con- 
tinent at average velocities of 25 to 30 miles per hour, or 600 
to 700 miles per day. 

The winds accompanying these cyclonic movements are the 
only permanent winds with which we, in the United States, are 

concerned. They are the winds 
that determine our weather, our 
rainfall, our floods and our 
droughts. 

Periodic Winds. — In addition 
to the permanent general circu- 
lation above discussed, there are 
certain periodic winds which are 
of considerable importance over 
restricted areas. Among these 
are the monsoons, land and sea 
breezes, mountain and valley 
breezes. 

Non-periodic. — In the region 
of the prevailing westerlies, cy- 
clones and anti-cyclones are oc- 
Wind Vane and Ane- casionally accompanied by high 
mometer. winds, such as the hurricane of 

the West Indies, the typhoon, the fohn, chinooks, blizzards 
and tornadoes. 

Anemometers. — Wind velocity is measured by the United 
States Weather Bureau, mainly by Robinson cup anemometers, 
illustrated in Fig. 21. These instruments are so placed as to 



Ball Bearings 
peciai Brass Coupling 



V/i Pipe 2 3 long 
2"x V/i Pipe Coupling 



I'ron Pipe 

Iron Step 
2° Pipe 12'0*long 
Contact Box 

Contacts 
— Iron Step 

2Pipe i long 
Iron Step 



Fig. 21. 



THE ATMOSPHERE 



37 



CD 9 































































Average 














































































































































- 




























































































































1 














































1 








Minnesota 




































1 




























































































































































vy 














































North Dakota 




















































































































































































Missouri 






























































































































































































— " 






















































Illinois 












































































































































































































































Ohio 


























































































































































































New York 
































































































































































































































*-*^~ 














































| Tennessee 


































































































































































































































Pennsylvania 
















































































































































































































































Georgia 















































































































































Jan. Feb. Mar. Apr. May June July Aug. Sept. Oct. Nov. Dec. 

Fig. 22. — Monthly Mean Wind Velocities at Continental Stations in the 

United States. 



38 ELEMENTS OF HYDROLOGY 

record approximately the wind velocity at an elevation of about 
30 feet above the general level of the surrounding country. 

Mean Wind Velocities in the United States. — Fig. 22 gives 
the monthly mean wind velocity at typical stations in various 
parts of the United States. In the Northwest the highest 
average wind velocity occurs in the spring, at a time when the 
temperature is rising. This results in very high rates of evapo- 
ration immediately preceding and during the spring break-up, 
and accounts, in a measure, for the disappearance of the winter 
snowfall and the freedom from extreme floods experienced by 
the Northwestern States at times when all other conditions are 
favorable for high water. 



CHAPTER III 

WATER: ITS VARIOUS STATES AND THEIR 
PROPERTIES 

Composition. — Water in the chemically pure state of the 
composition H 2 is not found in nature. As it occurs on the 
surface of the earth, water always contains more or less organic 
and inorganic material in solution and suspension. The im- 
portance to be attached to the impurities contained in water 
depends upon the contemplated use of the water. To be de- 
sirable for domestic purposes, water must be of a high standard 
of purity, not only as to chemical constituents, vegetable and 
animal matter carried, but also as to odor, color and taste. To 
be desirable for steam making, condensing and allied purposes, 
water should be reasonably free from sediment and incrustating 
materials. To be useful for power and navigation purposes, 
water may be of almost any degree of impurity, although the 
water of streams having their source in glaciers may contain 
sediment to an extent sufficient to make it unfit even for use in 
water-power development. In high-head projects provision must 
often be made for screening and sedimentation to prevent exces- 
sive wear on the water-wheels. 

Physical Properties. — Perhaps the one most important physi- 
cal property of water is its expansion upon freezing. Water in- 
creases in density until a temperature of 39.2° F. or 4° C. is 
reached, after which it slowly expands until at 32° F. or 0° C. 
upon solidifying, it expands about 10 per cent. After solidifica- 
tion, it again contracts, i.e., increases in density, with decrease 
in temperature. 

The effect of temperature and pressure on the state of water is 
shown in Fig. 23. 

39 



40 



ELEMENTS OF HYDROLOGY 



£20 
o 



no 



























EFFECT 

OF TEMPERATURE 

AND PRESSURE 

ON 

STATE OF WATER 
























































Liq 


lid 










Solk 




































c 

V 




























Vapor 


























Hoar 


Fr< 


st Li 


!2»»^ 










1 



The water occurring in the earth's atmosphere as vapor in 
spring and fall when the night temperature reaches the freezing 
point cannot be under a pressure exceeding the maximum pressure 

of saturated vapor, which is .18 

30 1 n — i 1 1 1 1 i i — I — 

inch mercury at 32° F. Under 
such conditions water can pass 
directly from the vaporous state 
to the solid state resulting in 
the familiar phenomena of hoar 
frost and snow. Similarly, ice 
and snow at temperatures below 
freezing readily pass from the 
solid to the vaporous state. 

A body of water cooling down 

in the fall maintains a reasonably 

so 75 loo 125 150 175 20o"~225 uniform temperature throughout 

Temperature - Degrees Fahrenheit 

F G 23 until it is cooled down to 39.2° F. 

Upon further cooling, the cold 
water, being lighter, remains at the surface where cooling then 
proceeds rapidly until ice is formed. The liberation of latent 
heat during the formation of ice somewhat retards the further 
cooling. Ice at 32° F. being about 10 per cent lighter than 
water at the same temperature floats upon the surface and 
thickens with continued low temperatures, thus maintaining a 
temperature of substantially 39° F. in the entire body of water 
beneath the ice and preserving animal life. 
j If water is kept in a perfectly quiet condition, it can be cooled 
down to about 20° F. before ice forms. Upon freezing, however, 
the temperature immediately rises to 32° F. on account of the 
heat liberated in the process of congelation. 

Frazil. — In flowing streams, where the velocity of the water 
is sufficient to prevent the formation of surface ice, " frazil " or 
" slush ice " will often be formed. Frazil consists of fine ice 
crystals, often several million to the cubic foot, that are carried 
along by the currents and, when present in large quantities, give 



WATER 41 

water a turbid appearance. Frazil forms most freely in flowing 
water on cold, cloudy days with an upstream wind. It never 
forms under ice cover, but the crystals are carried under 
the ice covering the quieter water, adhere to the sheet of ice 
above and accumulate at times until the entire channel is 
obstructed. 

Anchor Ice. — On cold clear nights, when the radiation of heat 
from the surface of the earth is very rapid, ice needles known as 
" anchor ice," closely resembling frazil in appearance, form, par- 
ticularly on dark-colored objects, on the beds of rather shallow, 
open bodies of water. Crystals of frazil floating in the water 
become entangled in the anchor ice formed on the bed of the 
stream and help to build up the mass. During the daytime the 
heat of the sun detaches anchor ice and brings it to the surface 
where it floats away, usually to become lodged under the ice 
cover of quieter water. 

Anchor ice, and particularly frazil, often seriously obstruct 
canals and penstocks and require careful consideration in the 
design of works for the utilization of water in cold climates. 

Elasticity. — The modulus of elasticity of water is approxi- 
mately 295,000 lb. per square inch or -nr<r that of steel, and it 
transmits sound and stress at the rate of substantially 4700 feet 
per second as against a rate of transmission of 1050 feet per 
isecond for air at 0° F. 

Weight. — The weight of pure water at 39.2° F. is 62.4 lb. per 
cubic foot. At boiling temperatures, the weight has decreased 
to 59.7 lb. per cubic foot. Mineral spring waters weigh as high 
as 62.7 lb.; sea water 64 lb.; and the water of the Dead Sea and 
Great Salt Lake, Utah, weighs as much as 73 lb. per cubic foot. 
For ordinary computations, the weight of fresh surface waters 
may be taken as 62.5 lb. per cubic foot. This is substantially 
correct and is often a convenient figure because it represents just 
1000 ounces avoirdupois. 

Steam. — At temperatures of 100° C. or 212° F. under stand- 
ard atmospheric pressure, water, upon the application of sufficient 



42 



ELEMENTS OF HYDROLOGY 



heat, passes freely from the liquid to the gaseous state known as 
steam, with an increase in volume of 1658 times. 

Specific Heat. — To raise the temperature of 1 gram of water 
1° C. requires the application of one calorie unit of heat. Simi- 
larly, to raise 1 lb. of water 1° F. requires the application of 
1 British thermal unit (B.t.u.) of heat. In other words, the heat 
required to raise the temperature of a unit volume of water 
1 degree is really the measure of these heat units. 

The heat required to raise the temperature of a given weight 
of water 1 degree would raise the temperature of the same weight 
of ice 2 degrees, of brick, or stone, about 5 degrees, and of iron or 
steel, about 9 degrees. 

The tremendous capacity of water for storing heat energy is 
graphically shown in Fig. 24. 



21000 




i — I — i — i — i — r 

Steam, Constant Volume - 



Steam, Constant Pressure - 



HEAT ABSORBING CAPACITIES 

OF 

WATER AND OTHER SUBSTANCES 



no a 



240 ■§ 

HO g 

.40 §? 
-32 Q 

-fio L 



< 100 .200 300 400 500 600 700 800 900 1000 1100 1200 1300 1400 1500 1600 1700 1800 1900 2000 
_Heat -British Thermal Units per Pound 

Fig. 24. 

Heat of Vaporization. — To change one gram of water at 
ordinary boiling temperature into one gram of vapor, or steam, 
at the same temperature, requires the expenditure of 536 calories 
of heat. To effect the same change in 1 lb. of water requires 970 
B.t.u. 

Heat of Fusion. — When 1 gram of water changes from the 
liquid state at 0° C. to the solid state, 80 calories of heat are 
liberated; similarly, when 1 lb. of water changes to ice, 144 
B.t.u. are liberated. The heat so liberated warms the water and 
thus tends to reduce the amount of freezing. 



WATER 43 

The Vapor of Water and Its Condensation 

Characteristics of Water Vapor. — Water in the gaseous state 
has a specific gravity of .622 as compared with dry air and con- 
forms approximately, though not exactly, to Boyle's law, which 
states that if the temperature of a gas is kept constant, the prod- 
uct of its pressure times its volume also remains constant. Water 
vapor also roughly obeys Charles' or Gay-Lussac's law, which 
states that if the volume of a gas is kept constant, the pressure 
which it exerts against the walls of its container decreases in 
direct proportion to the change in temperature measured from 
what is known as " absolute zero," i.e., a temperature of 273 de- 
grees below zero, Centigrade, at which all molecular motion is 
believed to cease. As water does not turn freely into the gaseous 
state at temperatures below 100° C, under normal barometric 
pressure, whereas the other gases of the atmosphere vaporize 
freely at temperatures far below those of the coldest outside air, 
it might be expected that the nearly saturated vapor of water 
would, in its behavior, , deviate somewhat from Boyle's and 
Charles' laws. 

Vapor Pressure. — If a drop of water, so small as to be scarcely 
visible, were introduced into the vacuum over the mercury of a 
barometer at a temperature of, say, 80° F., the water would turn 
into vapor and depress the mercury column about 1 inch. The 
further addition of small globules of water would not result in 
further vaporization or further depression of the mercury column 
except for the scarcely perceptible volume of the liquid added. 
Now, the actual weight of the added globule of water was negli- 
gible, especially when compared with a liquid 13.6 times as heavy, 
yet it depressed the column of mercury about an inch, i.e., it 
exerted a pressure on the top of the mercury column equal to a 
depth of over 1 foot of water. This pressure which the water 
in its gaseous state exerts is variously called " vapor pressure," 
" vapor tension," " elastic pressure " and " gaseous pressure." 
It is the same kind of pressure as that exerted by steam in the 



44 ELEMENTS OF HYDROLOGY 

cylinders of an engine. This vapor pressure or gaseous pressure 
is a function of the temperature. 

If, now, the temperature of the water on top of the mercury 
is raised to 100° F., more of the water will vaporize and the mer- 
cury column will be depressed about 2 inches. If the tempera- 
ture is raised to 150° F. the mercury column will be depressed 
about 7.5 inches and if the temperature is raised to slightly above 
212° F. the mercury column will be depressed the full 30 inches, 
i.e., the vapor pressure of the water will be exactly equal to the 
pressure of the atmosphere and the liquid will " boil " — vaporize 
freely — until it has all changed its state. 

If, instead of heating the water over the mercury column, we 
had lifted the barometer tube partly out of its cup so as to in- 
crease the space above the column of mercury, some water would 
have vaporized, but the height of the mercury column above the 
surface of the mercury in the cup would have remained the same, 
until saturation. 

Distribution of Water Vapor. — In the free air of the earth the 
water vapor exists in an almost saturated form, and its dis- 
tribution is dependent mainly upon temperature and convection 
currents. The elastic pressure of water vapor is a reasonably 
accurate measure of the weight of a unit volume of vapor, but it 
is not, by any means, a measure of the weight, on a unit area, of 
the entire column of vapor above that area. 

Relation of Vapor Pressure to Weight of Vapor. — If water 
vapor followed Boyle's law exactly, the weight of vapor in 
a given volume would be directly proportional to the elastic 
pressure exerted by the vapor at the same temperature. Ac- 
cording to Marvin : * 

„,..,„ . . ( vapor pressure in inches mercury) 
Weight ol vapor in grains T — r~r ~i = — rr 

percu.it. = n.7449 ((, + .002037 { ^^-32})/" 

* Marvin, C. F., Professor of Meteorology, U. S. Weather Bureau, in 
"Psychrometric Tables," 1912. 



WATER 45 

Table 2 gives the weight of a cubic foot of water vapor at 
different temperatures and percentages of saturation. 

Change in Vapor Pressure with Temperature. — Table 3 
gives the elastic pressure, in inches mercury, as determined 
experimentally by Regnault and Marvin, of saturated vapor at 
various temperatures. Values below 32 degrees differ substan- 
tially from those given by Broch. Above 32 degrees, Broch's 
and Marvin's values are identical. 



46 



ELEMENTS OF HYDROLOGY 



TABLE 2. —WEIGHT OF A CUBIC FOOT OF AQUEOUS VAPOR 
AT DIFFERENT TEMPERATURES AND PERCENT- 
AGES OF SATURATION 









(U 


. S. Weather Bureau 


) 








Temp., 


Percentage of saturation 


° F. 


10 


20 


30 


40 


50 


60 


70 
grains 


80 


90 


100 




grains 


grains 


grains 


grains 


grains 


grains 


grains 


grains 


grains 


-20 


0.017 


0.033 


0.050 


0.066 


0.083 


100 


0.116 


0.133 


149 


0.166 


-19 


0.017 


0.035 


0.052 


070 


0.087 


104 


0.122 


0.139 


0.157 


174 


-18 


018 


0.037 


0.055 


0.074 


0.092 


0.110 


129 


147 


0.166 


184 


-17 


0.020 


0.039 


059 


0.078 


0.098 


0.118 


0.137 


157 


0.176 


196 


-16 


0.021 


0.041 


0.062 


0.083 


0.104 


0.124 


0.145 


0.166 


0.186 


0.207 


-15 


0.022 


044 


0.065 


0.087 


0.109 


131 


0.153 


0.174 


0.196 


218 


-14 


023 


0.046 


0.069 


0.092 


0.116 


0.139 


0.162 


185 


0.208 


0.231 


-13 


0.024 


0.049 


0.073 


0.097 


0.122 


0.146 


170 


194 


0.219 


243 


-12 


026 


0.051 


0.077 


0.103 


0.128 


0.154 


0.180 


206 


231 


257 


-11 


0.027 


0.054 


0.081 


0.108 


0.135 


0.162 


0.189 


0.216 


0.243 


0.270 


-10 


0.028 


0.057 


086 


0.114 


0.142 


0.171 


0.200 


228 


0.256 


285 


- 9 


030 


0.060 


090 


0.120 


0.150 


0.180 


0.210 


240 


0.270 


0.300 


- 8 


0.032 


0.063 


095 


0.126 


0.158 


190 


221 


253 


284 


316 


- 7 


0.033 


0.066 


0.100 


0.133 


0.166 


0.199 


0.232 


266 


0.299 


0.332 


- 6 


0.035 


0.070 


0.105 


0.140 


0.175 


0.210 


0.245 


0.280 


0.315 


0.350 


- 5 


037 


0.074 


0.111 


0.148 


0.185 


0.222 


0.259 


0.296 


0.333 


370 


- 4 


0.039 


0.078 


0.117 


0.156 


0.194 


0.233 


0.272 


311 


0.350 


0.389 


- 3 


041 


0.082 


0.123 


0.164 


206 


0.247 


0.288 


329 


370 


0.411 


- 2 


0.043 


0.087 


130 


0.174 


217 


260 


0.304 


347 


0.391 


434 


- 1 


0.046 


0.091 


0.137 


0.183 


0.228 


0.274 


0.320 


0.366 


0.411 


0.457 





0.048 


0.096 


0.144 


0.192 


240 


0.289 


0.337 


385 


0.433 


481 


+ 1 


050 


0.101 


0.152 


0.202 


252 


0.303 


0.354 


404 


454 


0.505 


2 


053 


0.106 


0.159 


0.212 


264 


0.317 


0.370 


0.423 


0.476 


0.529 


3 


0.055 


0.111 


166 


0.222 


277 


0.332 


0.388 


443 


0.499 


0.554 


4 


0.058 


0.116 


0.175 


0.233 


0.291 


0.349 


0.407 


466 


0.524 


0.582 


5 


0.061 


0.122 


0.183 


244 


305 


0.366 


427 


0.488 


549 


610 


6 


064 


0.128 


0.192 


0.256 


0.320 


0.383 


0.447 


511 


0.575 


0.639 


7 


0.067 


0.134 


0.201 


0.268 


0.336 


0.403 


470 


0.537 


604 


671 


8 


0.070 


0.141 


0.211 


0.282 


352 


0.422 


0.493 


0.563 


634 


704 


9 


0.074 


0.148 


0.222 


0.296 


0.370 


0.443 


0.517 


0.591 


0.665 


0.739 


10 


078 


0.155 


0.233 


310 


0.388 


466 


543 


0.621 


698 


776 


11 


082 


0.163 


0.245 


0.326 


408 


0.490 


0.571 


653 


0.734 


816 


12 


086 


0.171 


0.257 


342 


0.428 


0.514 


599 


0.685 


770 


0.856 


13 


0.090 


0.180 


0.269 


0.359 


449 


0.539 


629 


718 


0.808 


898 


14 


094 


0.188 


0.282 


0.376 


470 


0.565 


0.659 


0.753 


0.847 


941 


15 


0.099 


0.197 


296 


0.394 


0.493 


0.592 


0.690 


0.789 


887 


986 


16 


0.103 


0.206 


0.310 


413 


0.516 


0.619 


0.722 


0.826 


929 


1.032 


17 


108 


0.216 


0.324 


0.432 


0.540 


0.648 


756 


0.864 


0.972 


1 080 


18 


0.113 


0.226 


0.338 


0.451 


0.564 


0.677 


0.790 


902 


1.015 


1 128 


19 


0.118 


0.236 


0.354 


0.472 


0.590 


0.709 


0.827 


0.945 


1.063 


1.181 


20 


0.124 


0.247 


0.370 


0.494 


0.618 


741 


0.864 


0.988 


1.112 


1.235 


21 


0.129 


0.259 


0.388 


0.518 


0.647 


0.776 


0.906 


1.035 


1.165 


1.294 


22 


136 


0.271 


0.406 


0.542 


0.678 


813 


0.948 


1.084 


1.220 


1.355 


23 


0.142 


0.284 


0.425 


0.567 


0.709 


851 


0.993 


1 . 134 


1.276 


1.418 


24 


0.148 


0.297 


0.445 


0.593 


0.742 


890 


1.038 


1.186 


1.335 


1.483 


25 


0.155 


0.310 


0.465 


0.620 


0.776 


931 


1.086 


1.241 


1.396 


1.551 


26 


0.162 


0.325 


0.487 


0.649 


0.812 


0.974 


1 . 136 


1.298 


1 461 


1.623 


27 


0.170 


0.339 


0.509 


0.679 


0.848 


1.018 


1.188 


1.358 


1.527 


1.697 


28 


0.177 


0.355 


0.532 


0.709 


0.886 


1.064 


1.241 


1.418 


1.596 


1.773 


29 


0.185 


0.371 


0.556 


0.741 


0.926 


1.112 


1.297 


1.482 


1.668 


1.853 


30 


0.194 


0.387 


0.580 


0.774 


0.968 


1.161 


1.354 


1.548 


1.742 


1.935 


31 


0.202 


0.404 


0.607 


0.809 


1.011 


1.213 


1.415 


1.618 


1.820 


2.022 


32 


211 


0.422 


0.634 


845 


1.056 


1.268 


1.479 


1.690 


1 902 


2.113 


33 


0.219 


0.439 


0.658 


0.878 


1.097 


1.316 


1 536 


1 . 755 


1.975 


2.194 


34 


0.228 


0.456 


0.684 


0.912 


1.140 


1.367 


1 595 


1.823 


2.051 


2.279 


35 


0.237 


0.473 


0.710 


0.946 


1.183 


1.420 


1.656 


1.893 


2.129 


2.366 


36 


0.246 


0.491 


0.737 


0.983 


1.228 


1.474 


1.720 


1.966 


2.211 


2.457 


37 


0.255 


0.510 


0.765 


1.020 


1.275 


1 530 


1.785 


2.040 


2.295 


2.550 


38 


0.265 


0.529 


0.794 


1.058 


1.323 


1.588 


1.852 


2.117 


2.381 


2.646 


39 


0.275 


0.549 


0.824 


1.098 


1.373 


1.648 


1.922 


2.197 


2 471 


2.746 


40 


0.285 


0.570 


0.855 


1.140 


1.424 


1.709 


1.994 


2.279 


2.564 


2.849 


41 


0.296 


0.591 


0.886 


1.182 


1.478 


1.773 


2.068 


2.364 


2.660 


2.955 


42 


0.306 


0.613 


0.919 


1.226 


1.532 


1.838 


2.145 


2.451 


2.758 


3.064 


43 


0.318 


0.635 


0.953 


1.271 


1.588 


1.906 


2.224 


2.542 


2.859 


3.177 


44 


0.329 


0.659 


0.988 


1.318 


1.647 


1.976 


2.306 


2.635 


2.965 


3.294 



WATER 



47 



TABLE 2. — WEIGHT OF A CUBIC FOOT OF AQUEOUS VAPOR 

AT DIFFERENT TEMPERATURES AND PERCENTAGES 

OF SATURATION. — Continued 

(U. S. Weather Bureau) 



Temp., 


Percentage of saturation 


°F. 


10 


20 


30 


40 


50 


60 


70 


80 


90 


100 


, 


grains 


grains 


grains 


grains 


grains 


grains 


grains 


grains 


grains 


grains 


45 


341 


683 


1 024 


1 366 


1.707 


2.048 


2.390 


2.731 


3 073 


3 414 


46 


354 


0.708 


1 062 


1.416 


1.770 


2.123 


2.477 


2 831 


3.185 


3.539 


47 


0.367 


733 


1.100 


1 467 


1 834 


2 200 


2.567 


2.934 


3 300 


3.667 


48 


0.380 


760 


1 140 


1 520 


1.900 


2.280 


2.660 


3 040 


3 420 


3.800 


49 


0.394 


0.787 


1.181 


1.574 


1.968 


2.362 


2.755 


3.149 


3.542 


3.936 


50 


408 


815 


1 223 


1 630 


2.038 


2 446 


2.853 


3 261 


3 668 


4.076 


51 


9.422 


844 


1 267 


1 689 


2.111 


2 533 


2.955 


3.378 


3.800 


4 222 


52 


437 


874 


1.312 


1 749 


2.186 


2 623 


3 060 


3 498 


3 935 


4 372 


53 


0.453 


905 


1 358 


1 810 


2 263 


2 716 


3 168 


3.621 


4 073 


4 526 


54 


468 


937 


1.406 


1.874 


2 342 


2 811 


3 280 


3.748 


4 216 


4 685 


55 


0.485 


970 


1.455 


1 940 


2 424 


2 909 


3 394 


3.879 


4 364 


4 849 


56 


502 


1.003 


1.505 


2 006 


2 508 


3.010 


3 511 


4 013 


4 514 


5.016 


57 


0.519 


1.038 


1 557 


2.076 


2 596 


3.115 


3 634 


4 153 


4 672 


5.191 


58 


537 


1 074 


1.611 


2 148 


2.685 


3 222 


3 759 


4 296 


4 833 


5.370 


59 


556 


1.111 


1 666 


2 222 


2.778 


3 333 


3 888 


4 444 


5 000 


5 555 


60 


574 


1 149 


1 724 


2 298 


2.872 


3 447 


4.022 


4 596 


5.170 


5.745 


61 


594 


1 188 


1.782 


2.376 


2.970 


3 565 


4.159 


4 753 


5.347 


5.941 


62 


614 


1 228 


1 843 


2.457 


3 071 


3 685 


4 299 


4.914 


5 528 


6.142 


63 


635 


1 270 


1 905 


2 540 


3.174 


3 809 


4 444 


5 079 


5 714 


6.349 


64 


656 


1.313 


1 969 


2.625 


3.282 


3 938 


4 594 


5 250 


5.907 


6.563 


65 


0.678 


1.356 


2 035 


2 713 


3 391 


4 069 


4.747 


5.426 


6 104 


6.782 


'66 


701 


1 402 


2 103 


2 804 


3 504 


4 205 


4 906 


5 607 


6.308 


7.009 


67 


0.724 


1.448 


2.172 


2.896 


3.620 


4 345 


5.069 


5 793 


6 517 


7.241 


68 


0.748 


1.496 


2 244 


2 992 


3 740 


4 488 


5 236 


5 984 


6.732 


7 480 


69 


0.773 


1.545 


2.318 


3.090 


3 863 


4.636 


5.408 


6.181 


6 953 


7.726 


70 


798 


1.596 


2 394 


3 192 


3 990 


4.788 


5 586 


6.384 


7.182 


7.980 


71 


824 


1 648 


2.472 


3 296 


4 120 


4 944 


5.768 


6 592 


7.416 


8.240 


72 


851 


1.702 


2.552 


3 403 


4 254 


5 105 


5.956 


6 806 


7.657 


8.508 


73 


878 


1 756 


2 635 


3 513 


4.391 


5.269 


6 147 


7 026 


7.904 


8.782 


74 


0.907 


1.813 


2.720 


3 626 


4.533 


5.440 


6 346 


7 253 


8.159 


9.066 


75 


0.936 


1.871 


2 807 


3 742 


4.678 


5.614 


6 549 


7 . 485 


8.420 


9.356 


76 


966 


1.931 


2 896 


3 862 


4.828 


5.793 


6 758 


7.724 


8.690 


9.655 


77 


0.996 


1 992 


2.989 


3.985 


4.981 


5.977 


6 973 


7 970 


8 966 


9 962 


78 


1 028 


2.055 


3.083 


4.111 


5.138 


6.166 


7.194 


8 222 


9 249 


10 277 


79 


1 060 


2.120 


3 180 


4.240 


5.300 


6 361 


7.421 


8.481 


9.541 


10 601 


80 


1.093 


2.187 


3.280 


4 374 


5 467 


6.560 


7.654 


8 747 


9.841 


10.934 


81 


1.128 


2.255 


3 382 


4.510 


5.638 


6.765 


7.892 


9 020 


10.148 


11 275 


82 


1.163 


2.325 


3.488 


4.650 


5.813 


6.976 


8.138 


9.301 


10.463 


11.626 


83 . 


1.199 


2.397 


3.596 


4.795 


5.994 


7 192 


8 391 


9.590 


10.788 


11.987 


84 


1.236 


2.471 


3.707 


4.942 


6.178 


7.414 


8.649 


9.885 


11.120 


12.356 


85 


1.274 


2.547 


3.821 


5 094 


6.368 


7.642 


8.915 


10 189 


11.462 


12.736 


86 


1.313 


2.625 


3.938 


5 251 


6 564 


7.877 


9.189 


10 502 


11.814 


13.127 


87 


1 353 


2.705 


4 058 


5 410 


6.763 


8.116 


9.468 


10 821 


12.173 


13 526 


88 


1.394 


2.787 


4.181 


5.575 


6.968 


8.362 


9.756 


11 150 


12.543 


13.937 


89 


1.436 


2.872 


4.308 


5.744 


7.180 


8.615 


10.051 


11.487 


12.923 


14.359 


90 


1.479 


2.958 


4 437 


5.916 


7.395 


8.874 


10 353 


11.832 


13.311 


14.790 


91 


1.523 


3.047 


4.570 


6.094 


7.617 


9.140 


10.664 


12.187 


13.711 


15.234 


92 


1.569 


3.138 


4 707 


6.276 


7.844 


9.413 


10.982 


12.551 


14.120 


15.689 


93 


1.616 


3.231 


4.846 


6 462 


8.078 


9.693 


11.308 


12.924 


14.540 


16.155 


94 


1.663 


3.327 


4.990 


6.654 


8.317 


9.980 


11.644 


13.307 


14.971 


16.634 


95 


1.712 


3.425 


5.137 


6.850 


8.562 


10.274 


11.987 


13.699 


15.412 


17.124 


96 


1.763 


3.525 


5.288 


7.050 


8.813 


10.576 


12.338 


14.101 


15.863 


17.626 


97 


1.814 


3.628 


5.443 


7.257 


9.071 


10.885 


12.699 


14.514 


16.328 


18.142 


98 


1.867 


3.734 


5.601 


7.468 


9.336 


11.203 


13.070 


14.937 


16 804 


18.671 


99 


1.921 


3.842 


5.764 


7.685 


9.606 


11.527 


13.448 


15 370 


17.291 


19.212 


100 


1.977 


3.953 


5 930 


7.906 


9.883 


11.860 


13.836 


15.813 


17.789 


19.766 


101 


2.034 


4.067 


6.100 


8.134 


10.168 


12.201 


14.234 


16.268 


18.302 


20 335 


102 


2.092 


4.183 


6.275 


8.367 


10.458 


12.550 


14.642 


16 734 


18.825 


20.917 


103 


2.151 


4 303 


6.454 


8.606 


10.757 


12.908 


15.060 


17.211 


19.363 


21.514 


104 


2.212 


4.425 


6.638 


8.850 


11.062 


13.275 


15.488 


17.700 


19.-912 


22.125 


105 


2.275 


4.550 


6.825 


9.100 


11.375 


13.650 


15.925 


18.200 


20.475 


22.750 


106 


2.339 


4.678 


7.018 


9.357 


11.696 


14.035 


16.374 


18.714 


21.053 


23.392 


107 


2 405 


4.809 


7.214 


9.619 


12.024 


14.429 


16.834 


19.238 


21.643 


24.048 


108 


2.472 


4.944 


7.416 


9.888 


12.360 


14.832 


17.304 


19.776 


22.248 


24.720 


109 


2.541 


5.082 


7.622 


10.163 


12.704 


15.245 


17.786 


20.326 


22.867 


25.408 


110 


2.611 


5.222 


7.834 


10.445 


13.056 


15.667 


18.278 


20.890 


23.501 


26.112 



48 



ELEMENTS OF HYDROLOGY 



TABLE 3. — ELASTIC PRESSURE OF SATURATED WATER 

VAPOR AT DIFFERENT TEMPERATURES 

(U. S. Weather Bureau; 



Air 


Vapor 


Air 


Vapor 


Air 


Vapor 


Air 


Vapor 


temp., 


press., 


temp., 


press., 


temp., 


press., 


temp., 


press. . 


T. 


in. Hg. 


°F. 


in. Hg. 


°F. 


in. Hg.' 


°F. 


in. Hg. 


-40 


0039 


5 


0.0491 


50 


0.360 


95 


1.645 


-39 


41 


6 


0.515 


51 


0.373 


96 


1.696 


-38 


44 


7 


0.542 


52 


0.387 


97 


1.749 


-37 


46 


8 


0.570 


53 


0.402 


98 


1.803 


-36 


48 


9 


0.600 


54 


0.417 


99 


1.859 


-35 


0.0051 


10 


0.0631 


55 


0.432 


100 


1 916 


-34 


54 


11 


0.665 


56 


0.448 


101 


1.975 


-33 


57 


12 


0.699 


57 


0.465 


102 


2.035 


-32 


61 


13 


0.735 


58 


0.482 


103 


2.097 


-31 


65 


14 


0.772 . 


59 


0.499 


104 


2.160 


-30 


0069 


15 


0.0810 


60 


0.517 


105 


2.225 


-29 


74 


16 


0.850 


61 


0.536 


106 


.2.292 


-28 


78 


17 


0.891 


62 


0.555 


107 


2.360 


-27 


83 


18 


0.933 


63 


0.575 


108 


2.431 


-26 


89 


19 


0.0979 


64 


0.595 


109 


2.503 


-25 


0.0094 


20 


0.103 


65 


0.616 


110 


2.576 


-24 


0.0100 


21 


0.108 


66 


0.638 


111 


2.652 


-23 


106 


22 


113 


67 


0.661 


112 


2 730 


- 22 


112 


23 


0.118 


68 


0.684 


113 


2.810 


-21 


119 


24 


0.124 


69 


0.707 


114 


2.891 


-20 


0.0126 


25 


0.130 


70 


0.732 


115 


2.975 


-19 


133 


26 


0.136 


71 


0.757 


116 


3.061 


-18 


141 


27 


0.143 


72 


0.783 


117 


3.148 


-17 


150 


28 


0.150 


73 


0.810 


118 


3.239 


-16 


159 


29 


0.157 


74 


0.838 


119 


3.331 


-15 


0.0168 


30 


0.164 


75 


0.866 


120 


3.425 


-14 


178 


31 


0.172 


76 


0.896 


121 


3.522 


-13 


188 


32 


0.180 


77 


0.926 


122 


3.621 


-12 


199 


33 


0.187 


78 


0.957 


123 


3.723 


-11 


210 


34 


0.195 


79 


0.989 


124 


3.827 


-10 


0.0222 ■ 


35 


0.203 


80 


1.022 


125 


3.933 


- 9 


234 


36, 


0.211, 


81 


1.056 


126 


4.042 


- 8 


247 


37 


219 


82 


1.091 


127 


4.154 


— 7 


260 


38 


0.228 


83 


1.127 


128 


4.268 


- 6 


275 


39 


0.237 


84 


1.163 


129 


4.385 


- 5 


0291 


40 


0.247 


85 


1.201 


130 


4.504 


- 4 


307 


41 


0.256 


86 


1.241 


131 


4.627 


- 3 


325 


42 


0.266 


87 


1.281 


132 


4.752 


- 2 


344 


43 


0.277 


88 


1.322 


133 


4.880 


- 1 


363 


44 


0.287 


89 


1.364 


134 


5.011 





0383 


45 


0.298 


90 


1.408 


135 


5.145 


+ 1 


403 


46 


0.310 


91 


1.453 


136 


5.282 


2 


423 


47 


0.322 


92 


1.499 


137 


5.422 


3 


444 


48 


0.334 


93 


1.546 


138 


5.565 


4 


467 


40 


0.347 


94 


1.595 


139 


5.712 



WATER 



49 



At 0° F. the vapor pressure is doubled for an increase of 13 
degrees in temperature. At 50 degrees it is doubled for an in- 
crease of 19 degrees, and at 100° F., the maximum vapor pressure 
is doubled for an increase of 23 degrees in temperature. At 
ordinary open-air tempera- 
tures, then, the elastic pres- 
sure of saturated water vapor 
is substantially doubled for 
every 20° F. increase in tem- 
perature. 

The amount of water vapor 
in the atmosphere may be 
determined directly with some 
form of dew-point apparatus, 
or indirectly by means of wet- 
and dry-bulb thermometers, 
or by . means of substances 
such as hair, wool, etc., which 
are sensitive to moisture. 

Dew-point Hygrometers. — 
All direct hygrometers utilize 
the principle that at a given 
temperature and pressure only 




Fig. 25. 



Typical Dew-point Ap- 
paratus. 



a certain definite amount of water vapor can occupy a given 
space, and that as soon as the space is saturated with moisture, 
dew will be deposited. 

Fig. 25 shows a typical dew-point apparatus. It consists 
essentially of: 

a. A thin polished silver cup, cemented upon the lower end 

of a glass tube, and rilled with some volatile liquid, such 
as sulphuric ether. 

b. A long tube joined to a rubber aspirator and extending 

through the stopper in the upper end of the glass tube 
to below the surface of the volatile liquid. 

c. A tube extending a short distance through the stopper, 



50 ELEMENTS OF HYDROLOGY 

and serving to carry off the fumes generated in the 
apparatus. 
d. A delicate thermometer extending through the stopper 
in the glass tube, and having its bulb immersed in the 
liquid. 

By means of the aspirator, air is forced through the tube (b) 
causing it to bubble up through the ether, vaporizing some of the 
ether, and, consequently, cooling the silver cup. The outside 
air coming in contact with the silver cup is cooled to the same 
temperature. When this temperature is sufficiently low so that 
the vapor in the outside air is condensed to the point of satura- 
tion, dew is deposited on the outside of the silver cup. The 
maximum vapor pressure which corresponds to the temperature 
at which dew will just deposit on the silver cup, represents the 
actual vapor pressure in the air at the time. The observer must 
refrain from breathing on the apparatus, but the air may ad- 
vantageously be given a very gentle motion by light fanning. 

Indirect hygrometers consist of wet- and dry-bulb thermome- 
ters, and of instruments depending for their action on substances 
such as hair, wool and certain mineral salts, which are sensitive 
to moisture. Hygrometers of the latter class do not give very 
accurate results, and need frequent comparison with wet- and 
dry-bulb hygrometers to make their readings of much value. 
Good hair hygrometers are the best instruments in this class. 

Wet- and Dry-bulb Hygrometers. — Indirect hygrometers, or 
psychrometers, utilizing wet- and dry-bulb thermometers in the 
determination of vapor pressure, depend upon the principle that 
evaporation results in cooling. The wet-bulb thermometer is 
wrapped with a silk or muslin wick, one end of which is immersed 
in distilled water. When air containing unsaturated vapor flows 
past the moist wick surrounding the wet-bulb thermometer, it 
absorbs some of the water in vapor form. The transformation 
of the water from the liquid to the vaporous state consumes heat, 
resulting in a reduction in the temperature of the moist wick, and 
its enclosed thermometer. 



WATER 



51 



By comparison of the depression of the temperature of the 
wet-bulb thermometer for given readings of the dry-bulb ther- 
mometer and a given barometric pressure, with simultaneous 
determinations of the temperature of the dew-point, by means 
of a dew-point apparatus, and a consideration of the funda- 
mental principles underlying the action of the wet- and dry-bulb 
thermometers, formulas have been derived and tables prepared 
from which the relative humidity, or the vapor pressure, may be 
read directly for a given depression of the wet-bulb thermometer 
and a given reading of the dry-bulb thermometer. 





Fig. 26. — Sling and Whirling Psychronietcrs. 

Stationary wet- and dry-bulb thermometers are frequently 
used indoors but do not give accurate results unless vigorously 
fanned before reading. Sling or whirling psychrometers are 
regularly used outdoors in the shelters at the telegraphic report- 
ing stations of the United States Weather Bureau at which 



52 



ELEMENTS OF HYDROLOGY 




WATER 53 

tvvice-a-day determinations of relative humidity are regularly 
made. 

Humidity. — Fig. 26 shows typical sling and whirling psy- 
chrometers. The ratio of the actual vapor pressure to the maxi- 
mum pressure of saturated vapor at the given air temperature 
constitutes the " relative humidity." The actual weight of 
water vapor per unit of volume is usually designated the " abso- 
lute humidity." 

Both relative and absolute humidity show considerable varia- 
tion with the seasons and in different localities, depending pri- 
marily upon the temperature and the moisture supply. The 
average relative humidity for the entire earth's surface is about 
80 per cent. The mean annual relative humidit}* - in the United 
States is shown in Fig. 27. High relative humidity is found along 
the seashore, and low relative humidity in the region east of the 
Rocky Mountains. 

Changes in relative humidity with season are graphically 
shown in Figs. 28 and 29. In general, the higher the temperature 
the lower the relative humidity, because of a prevailing deficiency 
in the supply of moisture. 

Figs. 30 to 38 show typical daily changes in air temperature, 
relative humidity and actual vapor pressure in Minnesota, in 
California and in the Panama Canal zone. 

A synopsis of weather conditions accompanies the graphs to 
permit of an intelligent study and interpretation of the data. 

Knowing the actual vapor pressure, the temperature of the 
dew-point can be readily determined. This temperature is of 
considerable importance, because it is substantially the limit to 
which the temperature of the night air may fall, because of the 
fact that the heat liberated when dew is deposited tends to pre- 
vent the temperature from falling below that of the dew-point. 

Fig. 14, p. 28, gives a typical graph of the variation in relative 
humidity with altitude up to an elevation of 10 miles. 

Density of Air. — The total weight of the air at sea level, as 
previously stated, is equivalent to the weight of 29.9 inches of 



54 



ELEMENTS OF HYDROLOGY 

































































































•^i - 










Average 
































































































































































































75 






















































Minnesota 


























































































60 


































































































75 
70 
65 
60 
80 
75 
70 
65 
60 
80 
75 
70 
65 
60 
80 
75 
70 
65 
60 

ao 




































































































North Dakota 




























































P" 










































































































































































Missouri 






















































































































































































Illinois 












































































































































































































































Ohio 








































































































































































































































75 
70 
65 
60 
SO 
75 
TO 
65 
CO 
80 
75 
70 
65 
60 












New York 












i 












































































































































































































































































Tennessee 


























































































































































































































































































Pennsylvania 






































80 
75 
70 
65 
BO 


















































































































































Georgia 












































" rr 









































Fig. 28. 



Jan. Feb. Mar. Apr. May June July Aug. Sept. Oct. Nov. Dec. 

Monthly Mean Relative Humidities at Continental Stations in 
the United States. 



WATER 



55 



mercury or 33.8 feet of water. The weight of a unit volume of 
air at sea level elevation and 0° C. is .00129278 times the weight 
of an equal volume of water. If the entire atmosphere, then, 
were of the same density as the air at sea level, the total depth 



80 

75 

70 

65 

60 

80 

75 

70 

65 

60 

.80 

§>75 

£70 

I 65 
£60 

i80 

£75 

2 70 
§65 
W 60 
£80 

3 ft 

I 70 
65 

60 

80 

75 

70 

65 

60 

80 

75 

70 

65 

60 



















































A 


vc 


ag 


e 






































































































































































































































































































Maine 




















































































| 
















































































































































































































Massachusetts 




























































































- 












































South Carolina 




































































































































































































































Florida 
























































































































































































, 












Texas 










































































































































































































































































































































California 










































1 1 1 









































Jan. Feb. Mar. Apr. May June July Aug. Sept. Oct. Nov. Dec. 



Fig. 29. — Monthly Mean Relative Humidities at Coastal Stations in the 

United States. 



of air covering the earth would be about 26,200 feet. On account 
of the elasticity and compressibility of the gases, however, the 
density decreases with altitude and the atmosphere extends to a 
much greater height than 5 miles. In a homogeneous atmosphere 



56 



ELEMENTS OF HYDROLOGY 



of uniform density, the reduction in pressure would be in direct 
proportion to the increase in altitude. In the atmosphere of the 
earth the reduction in pressure becomes continually less for every 
succeeding uniform increase in altitude. This fact is illustrated 
in Fig. 14, p. 28. 



100 



90 



60 



50 



I 

^ . 40 

7* s ' 30 

S5-; 

- £ S3 30 



































\ Ten 


iperature ^ 






















r Actu 


al Vapo 


■ Pressu 


re^^^/ 








































Re 


lative E 


umidity 






























































DAJLY VARIATION 

IN 

- AIR TEMPERATURE', RELATIVE HUMIDITY 

AND 

ACTUAL VAPOR PRESSURE 




Synopsis of Weather 

High barometrio pressure. Northerly 
winds shifting to southeasterly and 
increasing to 18 miles per hour. 50 per 




, _. 


MINNE 
- 


A 
APOLIS 
August 


T 
MINNE 
5, 1916 


SOTA. 






cent po 
cloudy 


ssible sunshine. Previous 
viih .42 inches rain. 

1 1 


day 



A.M. 



12 
Noon 



6 
P.M. 



12 



Fiu. 30. 



Specific Heat of Air. — Whenever a unit volume of dry air is 
permitted to expand under constant pressure, while being heated, 
.2375 unit of heat is required to raise its temperature 1° C. A 
little more than one quarter (.2867) of the heat energy applied 
is expended in the work of expansion, and the remainder (.7133 
or .1694 heat units) goes to heat the air. If the volume of the 
air is kept constant, only .1694 unit of heat is required to produce 
the same increase in temperature. The former figure is known 
as the specific heat of dry air at constant pressure, and the latter, 
as the specific heat at constant volume. 



WATER 



57 



100p 



80 



c 'JO 



T3 -w^ 



60 



3 " £? 

SSP 50 



40 



§ I 

a) £ 



S c m 

II a 20 

u ti ti 




DAILY VARIATION 

IN 

AIR TEMPERATURE, RELATIVE HUMIDITY 

AND 

ACTUAL VAPOR PRESSURE* 

AT 

MINNEAPOLIS, MINNESOTA. 

.August 6, 1916. 



Synopsis of Weather 



Fair day with about 90 per cent 6unshine 
Brisk southerly winds 18 miles per hour. 
Low pressure area from southwest pass 
ed almost directly overhead about 9 
p.m. resulting in drop in barometric 
pressure and wind velocity but no rain 
fell. Upward currents caused sudden 
reduction in actual vapor pressure. 



6 


s 


10 12 


A/M. 




Noon 

Fig. 31. 



6 
P.7M. 



ioo r 



<M 



,60 



H3 p< P50 



10 



30 



S 20 

s 

H 




< « 



10 



DAILY VARIATION 

IN' 

TEMPERATURE, RELATIVE HUMIDITY 

AND 

ACTUAL VAPOR PRESSURE 

AT 
MINNEAPOLIS, MINNESOTA. 
August 8, 1916. 
' I I L 



12 



6 
A.M. 



10 



12 
Noon 



Synopsis of Weather. 

Fair day with about 75 per cent sun- 
shine. High barometric pressure. 
Gentle northerly winds -5 miles per 
hour. No rain since August 4. 



6 
P.M. 



Fig. 32. 



58 



ELEMENTS OF HYDROLOGY 



80 



a 70 



S 
a 
o 

a s 

S -9 

a. es 

2g 8 60 

f s# 

B ft, ft 50 

u 

£2 i 
>- S 8 
° s S 
§•5 5 30 

>■ a> u 

_ S» 4) 

«:§ ft 

23 S 20 



































Temperature 














































































- 1 t^ A ctuaJ Vapor Pressure ., 






R 


elative ] 


[timidity ^^S- 






































DAILY VARIATION 

IN 

AIR TEMPERATURE, RELATIVE HUMIDITY 

AND 

ACTUAL VAPOR PRESSURE 




Synopsis of Weather 

Bright day with nearly 100 per cent Bun- 
shine. Brisk southerly winds increasing 
to 20 miles per hour in forenoon and de- 






MlNNE 


A 
APOLJ.S 
August 


T 

, MINNE 

9, 1916. 


SOTA. 






creasing to 15 miles per hour at suuset. 
Falling barometric pressure. 



A.M. 



10 12 

Noon 

Fig. 33. 



P.M. 



1» 



100 



90 



80 






"a 70 



W, 



2 S S 
£82 

a o ^-n 

ta fa ft so 



'40 



fa- 

u S © 
oat 

> gg 

a 3 a 
2.3E20 

O « 4> 

«<1«H 



10 











































"^X Te 


aperatui 


e 














^Act 


i&) Vapo 


r Pressu 


■e >^ 






.SI 

J 




Rel 


itive Hu 


midity - 
































































DAILY VARIATION 
I.N 

— AIR TEMPERATURE, RELATIVE HUMIDITY 

AND 
ACTUAL VAPOR PRESSURE 

— AT 
MINNEAPOLIS, MINNESOTA. 

August 10, 1916. 




Synopsis of Weather 

0.47 inches rain fell between 1 a.m. and 
3 a.m. Clearing during forenoon with 
75 per cent sunshine during afternoon 
Increasing barometric pressure. Variable 
southerly winds shifting to northwesterly 
and increasing to 20 miles per hour about 
6 p.m. 































So- 



li 



10 12 

Noon 

Fig. 34. 



is 



WATER 



59 



100 



<JO 



70 



g g60 



K a.0 



40 



fi a I 

u s jj 30 



■a £ §. 20 




10 



DAILY VARIATION 

IN 

AIR TEMPERATURE, RELATIVE HUMIDITY 

AND 

ACTUAL VAPOR FRESSURE 

AT 

MINNEAPOLIS, MINNESOTA. 

August 12, 1916. 



Synopsis of Weather 

Cold, cloudy day with 
no sunshine. 

Light showers. (Ot inch) 
about noon. 

Very high barometric 
pressure. 

Fresh northerly winds 

10 miles per hour. 



A.M. 



10 



12 
Noon 



6 
P.M. 



10 



12 



Fig. 35. 



100 



p. 90 



!70 



a 

.a 60 



;U0 



£50 a 50 



ft 

ho 



340 

tt 
I 



Sao -so 



u 20 3 20 



> I 
•3 10 



,10 





























































\jT 
























*fi 














- 






-sy 
V 




^ 


^ 


















=s42«a 


























^2£^ 


; ^^ 


















DAILY VARIATION 

IN 

AIR TEMPERATURE, RELATIVE HUMIDITY 

AND 

ACTUAL VAPOR PRESSURE 

AT 

DAVIS, CALIFORNIA. 

JULY, 1910. 

Data from Bulletin No.248 

Office of Experiment Stations 

U.S. Department of Agriculture 




























12 


> t 


( 


i 


i 1 


1 


2 2 






5 t 


1 


12 



P.M. 



Midnight 



Fig. 36. 



60 



ELEMENTS OF HYDROLOGY 



100 



90 



a o 70 



03 

U 

r 


c 
c 




00 






ti 








o 




E p* P 


50 


1 

a: 








E 


1 




41) 


£ 


p, 






Pj 


•a 


1 
u 


30 


5 








2. 


tt 






t> 


a 




« 






20 


B 


a 








O 




-U « 


H 










10 



13 



































^-- Actual Vapor Pressure 










































Air Terr 


perature^"'"- 


— "^^— Relative 


Humidity 




























































MEAN DAILY VARIATION 

IN 

IR TEMPERATURE, RELATIVE HUMIDm 

AND 

ACTUAL VAPOR PRESSURE 












A 


t 












AT 

ANCON CANAL ZONE 

WET SEASON 

Data from "The Panama Canal" 

by General Geroge W. Goethals 

191G 











































6 
P.M. 



12 

Noou 



6 
P.M. 



Fig. 37. 



100 



90 



£70 

a 
a 



W Oh P 






P. 2 

8, s 

a W 

> <a 

_ > 

a 33 



40 



30 



g,20 











































K-'Air T 


imperat 


ire 










/ 


r\> 




















5^ 
















^V^A 


ctual Va 


por Pres 


sure / 


















. Relati 


ve Hum 


dity y 




































MEAN DAILY VARIATION 

IN 

AIR TEMPERATURE, RELATIVE HUMIDITY 

AND 

ACTUAL VAPOR PRESSURE 

AT 

ANCON, CANAL ZONE 

DRY SEASON 






























Data fr 
by Gent 


)tn "The 

ral Gere 

IS 


Panama 
geW. G 
16 


Canal" 
oethalB 











A.M. 



10 12 

Noon 




P.M. 



Fig. 38. 



WATER 61 

Dynamic Cooling. — If, now, no heat is communicated to the 
air, and the pressure is reduced 3-73 part, the air will expand ^j^ 
part of its volume, and the heat used in the work of expansion 
will be drawn from the air itself, resulting in a cooling of .2867 
degree. To cool dry air 1° C. it must be permitted to expand 
7^f r part of its volume. In a homogeneous atmosphere of 
uniform, sea level density, a volume of air raised 100 meters 
would encounter a reduction of 78 1 2 ^ in pressure, resulting in a 
cooling of 1° C. Similarly a volume of air raised 185 feet would 
expand and cool 1° F. This assumes that the given volume of 
air would be raised so rapidly as not to receive heat from the sur- 
rounding air. 

The expansion of rising air containing unsaturated water 
vapor, by giving a larger space to the same number of molecules 
of vapor, results in a reduction in vapor pressure proportional to 
the reduction in barometric pressure. On the other hand, the 
cooling of the air with its vapor content, through the work of 
expansion, decreases its capacity for vapor to a greater extent, 
hence, condensation will ultimately occur. The distance in feet, 
which unsaturated water vapor must rise above the earth's 
surface to effect condensation of the vapor through the cooling 
resulting from expansion is approximately equal to 225 times the 
difference, in degrees Fahrenheit, between the ordinary air tem- 
perature and its dew-point temperature. 

Ascending air containing saturated water vapor cools much 
more slowly than dry air because the reduction in temperature 
results in a condensation of some of the vapor, and the heat so 
liberated supplies some of the heat required in the work of ex- 
pansion, thus preventing the air from cooling as rapidly as it 
otherwise would. The higher the temperature of the air the 
more water vapor it would contain at saturation, consequently, 
the slower it would cool upon rising. At sea-level, for example, 
saturated vapor at a temperature of 32° F. would cool 1° F. in 
rising 285 feet. If the temperature of the vapor is 68° F. it 
would cool 1 degree in rising 425 feet. At an elevation of about 



62 ELEMENTS OF HYDROLOGY 

2\ to 3 miles, where the maximum storm development occurs, 
vapor at a temperature of 50° F. would cool about 1 degree in 
rising 425 feet, because the same amount of heat liberated in 
condensation of vapor has a greater effect in preventing the cool- 
ing of the less dense air. 

Stable and Unstable Air. — Inasmuch as air containing satu- 
rated vapor, upon rising, cools 1 degree for about every 425 feet 
of ascent, and as the reduction in temperature of the undisturbed 
surrounding air averages 1 degree for every increase of about 300 
feet in altitude, it must be apparent that rising saturated air is 
continually warmer than the surrounding unsaturated air, and 
therefore has an increasing tendency to rise, with the resulting 
precipitation of its vapor content, i.e., such air is in unstable 
equilibrium. 

Air containing unsaturated water vapor, however, upon being 
given an impulse upward, cools 1 degree for the first 185 feet of 
ascent above the earth's surface; hence it quickly becomes cooler 
and consequently heavier than the surrounding undisturbed 
atmosphere and tends to fall back to its original position, i.e., 
such air is in stable equilibrium. 

Effect of Vapor on Weight of Air. — Since the specific gravity 
of water vapor is only a little more than six tenths of the specific 
gravity of dry air at the same temperature and pressure, it follows 
that the pressure of water vapor at a given temperature is greater 
than the pressure of an equal amount of dry air at the same 
temperature. At a temperature of 80° F., for example, the 
maximum elastic pressure of water vapor is equal to about 1 inch 
of mercury. A cubic foot of dry air at 80° F. and 30 inches 
barometric pressure weighs .0735 lb. If part of the air is replaced 
by water vapor under the same pressure until the space is sat- 
urated with vapor, about one thirtieth of the volume of air will 
be displaced. The elastic pressure will remain the same but the 
weight of the cubic foot of air and vapor will be reduced to 
.0726 lb. 

The weights of dry air and of air containing saturated water 



WATER 



63 



vapor at the given temperature, i.e., air at 100 per cent relative 
humidity, and under 30 inches barometric pressure, are graphi- 
cally shown in Fig. 39. 




0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 

"Weight -Pounds per Cubic Foot 

Fig. 39. — Effect of Temperature on Weight of Dry and Moist Air under 
Pressure of 30 Inches Mercury. 



CHAPTER IV 

PRECIPITATION: ITS OCCURRENCE AND 
DISTRIBUTION 

Dew and Frost. — Whenever the water vapor in the air is 
cooled down below the temperature corresponding to the pres- 
sure of saturated vapor, condensation occurs on dust parti- 
cles, globules of water, grass, or other foreign objects. 

During summer nights grass and other forms of vegetation, 
being good radiators of heat, soon cool down the surrounding 
air to a point where some of the moisture is precipitated out in 
the form of dew. If the dew-point temperature is below 32° 
F. and the night cool, moisture may be condensed out in the 
form of hoar frost. 

In arid regions dew is often an appreciable source of water 
supply for the scant vegetation found in such regions, as it 
forms mainly on the plants and not on the barren soil. 

Rain, Snow, etc. — Condensation of moisture out of the atmos- 
phere above the immediate surface of the earth occurs on dust 
particles or suspended globules of water and takes the form 
of fog, cloud, rain, snow or hail. The condensation which re- 
sults in the precipitation of moisture from clouds is caused by 
what is known as "dynamic cooling," i.e., the cooling resulting 
from the consumption of heat in the work of expansion of the 
rising vapor, as previously explained. 

It is a common misconception that almost all of the rain 

which falls on the land comes from moisture evaporated from 

the ocean. As a matter of fact, the greater portion of the 

rain which falls in the United States is water re-precipitated 

after having fallen as rain and having evaporated from the 

land area. Only that portion of the rainfall which runs off 

64 



PRECIPITATION 65 

through the streams back into the ocean represents water 
which was evaporated from the ocean. The remainder rep- 
resents rain which fell on the land, was evaporated from the 
land, condensed from the atmosphere over the land, and re- 
precipitated as rainfall. The portion of the rainfall which is 
derived from the moisture evaporated over the ocean varies 
in different parts of the country. In those regions where the 
prevailing winds are off the ocean, the greater portion of 
the rainfall naturally represents moisture evaporated from the 
ocean. Among such regions are the Pacific slope and the 
region bordering the Gulf of Mexico. The Upper Mississippi 
and Missouri valleys and the eastern slope of the Rocky 
Mountains are typical of the areas which derive most of their 
rainfall from moisture evaporated from the land. 

Convective Precipitation. — In the equatorial regions the 
principal air movement is vertical. The result of these vertical 
or convection currents is that the air in moving upward expands 
and cools, causing precipitation. The heating of the lower 
strata of air during the forenoon accentuates the upward move- 
ment, causing daily rains during the afternoon. The radiation 
of heat during the early evening usually arrests the convection 
currents, and results in a cessation of rainfall. 

Orographic Precipitation. — In the mountainous regions, such 
as on our Pacific Coast, the air is forced upward when it reaches 
the mountain ranges, expands, cools and precipitates its mois- 
ture. Fig. 40, from the June, 1914, Monthly Weather Review 
illustrates the formation of clouds and the precipitation of mois- 
ture in this manner. 

On the leeward side of the mountains, the air descends, absorbs 
moisture, and gives rise to arid regions. 

Cyclonic Precipitation. — As stated, briefly, on page 29, the 

unequal heating of the earth's land and water masses results 

in more or less permanent regions of high and low barometric 

pressure. This fact is shown in Figs. 41 and 42,* which give 

* Courtesy Ginn and Company. 



66 



ELEMENTS OF HYDROLOGY 



the mean sea level isobars, or lines of equal barometric pres- 
sure, for the world, during January and July. A mean differ- 
ence equal to about half an inch of mercury will be noted 
between the pressure over the oceans and over the land. This 
difference is sufficient to set the air masses in motion. 

The maximum development of storms is limited to an aver- 
age elevation of about three miles. 

W" ' 



\-\^M'§S§'^ ^ ! y:r'-'^' v v.;.'^; 



■iX&^-% 




Fig. 40. — Mount Lowe, Cal., during the Rain of February 20, 1914. 

Fig. 43 shows in a general way the mean tracks of the high- 
and low-pressure areas across the United States. Individual 
storms, of course, usually depart considerably from the mean 
tracks. This is well illustrated in Fig. 44 taken from " Weather 
Forecasting in the United States," U. S. Weather Bureau, 1916. 

The rate of translation of these storm centers depends upon 
the pressure gradient between them. The following table 
gives the wind velocity resulting from given differences in pres- 
sure between two localities 500 miles apart. 



Pressure gradient, 

inches mercury 

in 500 miles 


Wind velocity, 

miles per 

hour 


0.43 


10 


0.48 


15 


0.52 


22 


0.62 


30 


0.76 


35 




a 

M 



(67) 




(68) 



PRECIPITATION 



69 




Fig. 43. — Mean Tracks and Average Daily Movement of Storms in the 

United States. 




Fig. 44. — Paths of North Pacific Lows, January, 1900-1909. 



70 



ELEMENTS OF HYDROLOGY 



The monthly mean velocity of cyclones and anticyclones 
passing over the United States between 1878 and 1904 is shown 
in the following table: 

AVERAGE VELOCITY OF STORMS IN UNITED STATES 

U. S. Weather Bureau, 1878-1904 

(Velocity in miles per hour) 



1 


Jan. 

34.8 
29.5 


Feb. 

34.8 
28.2 


Mch. 

31.6 

26.7 


Apr. 

26.9 
25.2 


May 

24.3 
25.4 


June 

24.0 

23.7 


July 

24.4 

22.2 


Aug. 

24.6 
22.1 


Sept. 

24.8 
24.7 


Oct. 

27.4 
24.7 


Nov. 

30.7 

27.1 


Dec. 

34.9 
27.4 


Year 


Cvclones 

'(3276) 
Anticyclones 

(1587) 


28.6 
25.6 



" Lows." — An area over which low barometric pressure pre- 
vails is spoken of as a " low " or cyclonic " area, and one over 
which high barometric pressure prevails as a " high " or " anti- 
cyclonic " area. Cyclonic weather is characterized by increas- 
ing surface temperature, easterly winds increasing in intensity, 
decreasing barometric pressure, increasing cloudiness, and pre- 
cipitation. The air over a low-pressure area moves inward and 
upward, and, in the northern hemisphere, in more or less 
regular, counter-clockwise, rotary paths. The low-pressure 
areas are roughly circular and vary from about 500 to 1500 
miles in diameter. 

" Highs." — After the low area has passed the barometric 
pressure increases, the clouds break, the winds shift to the 
west, and anticyclonic weather sets in. Its characteristics 
are high barometric pressure, low temperature, clear skies, 
increasing westerly winds moving downward and outward 
from the center of the high-pressure area in approximately 
clockwise, rotary parts. 

As previously stated, temperature and pressure gradients be- 
tween land and water masses and between poles and equator, 
together with the rotation of the earth, give rise to the general 
circulation of the atmosphere. Cyclones and anticyclones ap- 
pear to be whirls of dynamic origin, in the larger air movements, 



PRECIPITATION 



71 



and not the result of local convection currents. Cyclonic 
activity is limited to the lower layer of air about five miles in 
thickness, above which the temperature changes are slight. 
In the upper levels of the fleecy, cirrus clouds there is the 
permanent eastward drift of air at velocities of about 90 miles 
per hour.* 

Thunderstorms. — During warm weather cyclonic areas are 
usually accompanied by thunderstorms. Fig. 45 taken from the 
Monthly Weather Review of June, 1914, is a typical diagram- 
matic representation of a thunderstorm, and Fig. 46 shows the 
changes in meteorological elements during such a storm. The 
upward rush of moist air in a cyclone results in the formation 
of the cumulus clouds typical of thunderstorms. 




Fig. 45. — Diagrammatic Representation of a Thunderstorm. A, ascending 
air; D, descending air; C, storm collar (Sturmkragen) ; S, roll scud; D, 
wind gust; H, hail; T, thunderheads; R, primary rain; R', secondary rain. 



A thunderstorm, as the name implies, is a storm accompanied 
by lightning and thunder and, usually, precipitation. Accord- 
ing to Simpson f the electricity whose discharge constitutes the 
lightning of the thunderstorm is generated by the breaking up 
of falling rain drops encountering strong upward currents. 
The resulting spray is carried upward and the small drops, 

* For a fuller discussion of this phase of the subject see Professor Bigelow's 
report, "The International Cloud Observations," Annual Report, Chief of 
Weather Bureau, 1898-1899, and Monthly Weather Review, November, 1914, 
and April, 1916. 

t Simpson, Dr. G. C, in Memoirs, Indian Meteorological Department. 



72 



ELEMENTS OF HYDROLOGY 



through coalescence, soon grow so large as to fall again. Coa- 
lescence and disruption proceed rapidly and the electrical charge 
within the cloud grows. The positive charge in the cloud 
draws an excess of negative electricity to the ground underneath 
or to a nearby cloud until a current of electricity, visible as 



6 7 8 9 10 11 Noon 


L 2 3 4 5 6 


















\ 






r" no 






6 






o 
£80 

b0 
<u 
Q 70 

"29.90 

1 29.80 

60 

50 
u 

J 40 

I 30 

1.20 

10 








—\ 


Ce^" 








\ 
























\ 
























/l-.- 


■ 












Pres 


sure 






s / 


|V» 


ls — 


■~^, 




















1 
























































































































V 


»— , k 










Wi 


DdV( 


locit 


? 








\ 


> 




2.0 

„1.5 

f 1.0 

H 

0.5 






























































t 


/ 






















I 






































Rair 


fall 







































MW NW N N N N NW WNSNNEESSWW 
Fig. 46. — Course of Meteorological Elements during a Thunderstorm at 
Washington, D. C. (July 30, 1913). 



lightning, flows through the intermediate air, heating it in 
its passage and setting up the familiar, violent sound wave 
through the sudden expansion of the heated air along the path 
of discharge. During thunderstorms, ozone, nitrous oxide and 
ammonia are produced and carried to earth by rain, adding 
in small though appreciable measure to the fertility of the soil. 
Thunderstorms occur with varying frequency both as to time 
and locality. South of latitude 40 degrees, excepting both 



PRECIPITATION 



73 



Atlantic and Pacific coasts where they occur less frequently, 
the average occurrence of thunderstorms is from 50 to 75 a year. 
By far the greater number occur between the months of April 
and September. In general the frequency varies from about 
75 a year in the Gulf region and in New Mexico to 20 a year 
along the northern border of the United States with less than 
10 a year, on an average, in the Pacific Coast states. 



190* 05 06 07 08 09 10 11 12 1913 



3 
H 40 



























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stor 


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a 
a 
i 

a 

810 •£ 

a 
820 !§• 

800 £ 

-80 § 



Fig. 47. 



Relation between Precipitation and Thunderstorms in the 
United States. 



Thunderstorms appear to be most frequent in years of high 
rainfall which, considering the world as a whole, are also warm 
years. Fig. 47 taken from the June, 1914, Monthly Weather 
Review shows the relation between the annual number of thun- 
derstorms and average annual precipitation at 127 stations in 
the United States. 



74 75 78 77 78 79 g 81 82 83 84 85 86 87 I 



91 92 93 94 95 96 97 98 I 



01 02 03 04 05 06 07 08 09 2 11 12 13 



si +1 - 5 ' 



o.g-1.0' 

& 1-1.5' 















, 










































































- 


■~. 












































































' 










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. 


















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~>P 


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v 


^ x^, 












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European Rainfall 


























































:.-i 


4( 


rn 


a 


K. 


T 


in 


po 


ra 


tir 


■- 


-- 


- 















■»# e ~ 



°" a a 

9^Q| 



Fig. 48. — Relation of Temperature in Eastern United States to Rainfall in 

Europe. 



Fig. 48 taken from the same source shows the relation be- 
tween the temperature in the Eastern United States and the 
rainfall in Europe. Both sets of curves are smoothed to elimi- 
nate minor irregularities. 



74 



ELEMENTS OF HYDROLOGY 




PRECIPITATION 



75 




- 



76 



ELEMENTS OF HYDROLOGY 




f!:tfHv* !S!reas 

plJlliliipifii 

sl = 5 s » Oils sll = 



lasii.-5#l3B|| 



PRECIPITATION 77 

Weather Forecasts. — Daily weather forecasts are made 
by the United States Weather Bureau on the basis of the pre- 
ceding twenty-four hours' observations at about 200 telegraphic 
reporting stations. These forecasts take the form of official 
statements of weather probabilities, weather maps, special 
warnings to lake and coasting vessels, flood warnings, instruc- 
tions to shippers, and the display of weather flags. All obser- 
vations used in forecasting the weather, such as observations 
of barometric pressure, temperature, direction and velocity of 
wind, relative humidity, precipitation and sunshine, are made 
at 8 a.m. and 8 p.m. 75 Meridian time, and the data are im- 
mediately telegraphed in cipher to the main office at Wash- 
ington and also to a number of large cities where forecasters 
are stationed. Here the data are quickly transferred to a base 
map, the forecasts made, and the " Daily Weather Map " im- 
mediately printed and placed in the mails so as to be avail- 
able for use by the general public as promptly as transportation 
facilities permit. 

Figs. 49 to 51 show typical " Daily Weather Maps " for 
February 11, 13 and 15, 1915, with the exception of the Min- 
neapolis local forecast and the record of observations at the 
principal telegraphic reporting stations. Except for the re- 
duction in scale and difference in drafting, these figures are 
exact copies of the actual daily weather maps issued by the 
local office on the given dates. The path of the dominating 
low-pressure area has been added to the maps to facilitate their 
study and interpretation. 

Any person thoroughly familiar with the phenomena and the 
principles that underlie our weather conditions can do consid- 
erable " forecasting," even without the aid of any instruments, 
by merely observing the outstanding weather characteristics 
in his locality. The wind is perhaps the best weather indicator. 
Its significance is succinctly stated on the " Daily Weather Map " 
in the following language: 



78 ELEMENTS OF HYDROLOGY 

Wind-Barometer Indications 

" When the wind sets in from points between south 
and southeast and the barometer falls steadily a storm 
is approaching from the west or northwest, and its 
center will pass near or north of the observer within 
12 to 24 hours with wind shifting to northwest by way 
of southwest and west. When the wind sets in from 
points between east and northeast and the barometer 
falls steadily a storm is approaching from the south or 
southwest, and its center will pass near or to the south 
or east of the observer within 12 to 24 hours with wind 
shifting to northwest by way of north. The rapidity 
of the storm's approach and its intensity will be indi- 
cated by the rate and the amount of the fall in the 
barometer." 

Measurement of Precipitation. — Precipitation is regularly 
recorded in the United States at nearly 6000 stations. Of 
these about 200 constitute the " regular " or " telegraphic- 
reporting " stations, at which a full record is kept of such 
meteorological phenomena as amount and rate of precipitation, 
temperature, relative humidity, direction and velocity of wind, 
sunshine, the occurrence of frosts, aurora, thunderstorms and 
the like. At most of the remaining stations, known as " coop- 
erative observer " stations, record is kept only of rainfall and 
snowfall, maximum and minimum temperature, and general 
information regarding such phenomena as frost, sunshine, 
auroras, and the like. 

Standard Rain Gage. — Cooperative observers are furnished 
with a standard rain gage, Fig. 52, and maximum and minimum 
thermometers. A typical cooperative observer station is shown 
in Fig. 6, page 20. 

The standard rain gage consists of a funnel-shaped collector 
A eight inches in diameter at the top, a measuring tube C, 
20 inches high and 2.53 inches in diameter, i.e., one tenth 



PRECIPITATION 



79 



FRONT VIEW VERTICAL SECTION 




standard rain gage 
Fig. 52. 



the area of cross section of the receiver, an overflow attach- 
ment B and a measuring stick graduated to read directly to 
inches depth of precipitation. 
Rain falling into the receiver 
A runs down through the small 
opening e into the measuring 
tube C where the depth can be 
measured with the graduated 
stick. If the rainfall exceeds 
2 inches, the measuring tube 
C overflows into B, from which 
the observer later refills the 
tube C for measurement. 

When used as a snow gage 
the funnel A and the measur- 
ing tube C are removed and the overflow cylinder B is used 
to catch the precipitation directly. 

Tipping-bucket Gage. — At the regular Weather Bureau sta- 
tions, where a continuous record 
of rainfall is obtained, a record- 
ing gage known as the " tipping- 
bucket " gage illustrated in Fig. 53 
is employed. Rain falling into the 
collector, which is 12 inches in diam- 
eter, runs into the bucket through 
a funnel attached to the bottom of 
the collector. The bucket is divided 
into two parts, and is mounted on 
trunnions so placed that when one 
part of the bucket is filled, it tips 
over and empties its contents into 
the reservoir below. The bucket is 
usually adjusted so that it tips for 
each one-hundredth inch rainfall. At high rates of rainfall, 
amounting to a bucketful every few seconds, a correction must 




Fig. 53. — Tipping-bucket Rain 



80 



ELEMENTS OF HYDROLOGY 



be made to the record because each bucket, during the tipping 
motion, becomes overfilled. By means of an electrical circuit 
which is closed and opened at each tip of the bucket, each one- 
hundredth inch of rain is recorded by a pen on a clock-operated 
record sheet. Check readings of the total amount of precipita- 
tion are made by measuring the water in the reservoir. 

Marvin Float Gage. — Another type of recording rain gage 
which has wide application is the Marvin float gage, illustrated 

in Fig. 54. An 8-inch collector 
protected by a 21-inch windshield 
gathers the rainfall into a reservoir. 
A record of the precipitation is se- 
cured by means of a float on the 
surface of the water in the reser- 
voir actuating a pen which traces 
the record on a clock-operated 
record sheet. The recording ap- 
paratus is contained in the square 
portion of the apparatus. An 
eight-day record is secured with- 
out attention and the precipitation 
can be estimated from the record 
sheet to hundredths of an inch. 
About one fourth inch of kerosene 
is kept on the water in the receiver to prevent evaporation. 
The gage has a total capacity of 10 inches rainfall and may be 
conveniently emptied through the spigot provided, which per- 
mits draining the receiver only to the point where the float 
has returned to the zero mark. 

A number of other automatic rain gages, used outside of the 
U. S. Weather Bureau, are on the market. 

Exposure of Rain Gage. — Rather more important than 
the selection of the rain gage, however, is the placing of it. 
The primary disturbing influence is the wind. The following 
table gives some observations of the decrease in the catch 




Fig. 54. — Marvin Float Gage 
with Wind Shield. 



PRECIPITATION 



81 



of the rain gage with increase in elevation of the gage above 
the surface of the ground, primarily, because of the effect of 
the wind at the higher levels. 



Elevation of 


Relative catch 


rain gage 


of rain gage 


Feet 







1.00 


43 


0.75 


85 


0.64 


194 


0.58 



In small towns the rain gage can usually be placed on the 
ground in an open lot surrounded by a fence or low bushes. 
No object near the gage should be within a distance equal to 
its height. The gage should, of course, be free from moles- 
tation. In the larger cities the rain gage 
is usually placed near the center of a 
large flat roof. The use of wind shields, 
such as that illustrated in Fig. 54, page 80, 
has been found to overcome most of the 
ill effects of the wind. This was forcibly 
presented, first, by Nipher in St. Louis, in 
1878, when he demonstrated that a gage, 
equipped with his shield, placed on an 
18-foot pole above the tower of the uni- 
versity, 118 feet above ground, collected 
the same amount of rainfall as a shielded 
gage placed on the ground. 

Measuring Snowfall. — The difficulties 
encountered in measuring rainfall are ac- 
centuated in measuring sleet and snowfall. 
Light snow is often blown out of the gage 
again by high winds even after having once lodged in the gage. 
The action of the ordinary snow gage during a snowstorm is 
well illustrated by Fig. 55 from an article by Horton.* 

* Horton, R. E. ( Monthly Weather Review, February, 1914, p. 99. 




Fig. 55. — Action of Or- 
dinary Snow Gage dur- 
ing Snowstorm (after 
Horton). 



82 ELEMENTS OF HYDROLOGY 

The catch of the gage in this case was only .43 inch although 
the total snowfall was 1.41 inches. 

The Weather Bureau has long required its observers to 
measure the snow upon the ground in one or more selected 
spots where experienced judgment indicates that a normal 
and representative depth of snowfall is to be found. Satis- 
factory locations are usually afforded by small open places 
in wooded parks, small clearings in deep woods with some 
underbrush or among rather open second growth. By using 
the gage as a " cookie cutter " a cylinder of new snow can be 
secured which can be melted by the addition of a known quantity 
of hot water and the equivalent rainfall determined. When- 
ever the snow is not melted or weighed its water equivalent 
is determined by the conventional ratio of ten volumes of snow 
to one volume of water. Although this constitutes a satisfactory 
average ratio, it deviates widely from the truth at times. In 
southern latitudes the snow is moist and a higher ratio usually 
applies. In the latitude of northern Minnesota the snowfall 
is usually lighter, and 11 to 12 inches and occasionally as high 
as 30 inches of new snow are required for one inch of water. 
As the percentage of precipitation which occurs as snow is 
usually ,quite small, however, the resulting error in annual pre- 
cipitation is much less than the probable error in the ratio 
might indicate. 

A map of the mean annual snowfall in the United States is 
given in Fig. 56. 

The great depth to which snow falls in places in the West is 
well illustrated in Fig. 57 taken from the May, 1915, Monthly 
Weather Review. 

When rain, sleet and snow occur together, or when the snow 
melts as it falls, ground measurements are obviously inap- 
plicable, and a shielded snow gage of the type illustrated in 
Fig. 58 must be resorted to. 

The best method of determining the water content of the 
total layer of snow on the ground at any time during the 



PRECIPITATION 



83 




84 



ELEMENTS OF HYDROLOGY 



season is by means of weighing a cylinder of snow cut from the 
snow layer by means of tubes. One type of tube in use by 




Fig. 57. — Snowfall at Hobart Mill, Cal. 




Fig. 58. — Marvin Shielded Snow Gage. 

the Weather Bureau is 2| inches in diameter and of varying 
length. One end of the tube is fitted with a toothed steel 
cutting edge. The outside is provided with a scale of inches. 



PRECIPITATION 



85 



Snow Surveys. — Snow surveys, made shortly before the 
spring break-up, are often of considerable service in the moun- 
tainous regions of the West in predicting the probable supply 
of water which will be available during the succeeding irriga- 




Fig. 59. — Apparatus used in Snow Surveys. 



tion season. The apparatus essential for such work is shown 
in Fig. 59 and the character of the country in which such 
surveys have been made, is shown in Fig. 60. The depth 
of snow, especially in rough country, is determined much more 
frequently than its density. On a topographic map or sketch 
of the region, the extent of snow cover is shown, together with 



86 



ELEMENTS OF HYDROLOGY 



the depth and density of the snow as determined by the survey. 
From these data the equivalent depth of rainfall over the entire 
area, and hence the approximate available water supply, is 
determined. 




Fig. 60. — Typical Country in which Snow Surveys were made. 



Variation of Character of Precipitation with Temperature. — 

Although the surface air temperature is not an unfailing indica- 
tion of the character of precipitation by any means, the Weather 
Bureau records indicate a reasonably constant relationship from 
year to year in the Northwest. 

Fig. 61 shows the monthly mean, and the mean maximum 



PRECIPITATION 



87 



3 &150 

2~ft 
H 

25 



-■= 20 



and minimum temperatures, and the approximate percentage 
of total precipitation which falls as snow during the various 
months of the year, at St. Paul and at Moorhead, Minn. For 
a monthly mean temperature of 
23 degrees, the mean of the max- 
imum daily temperatures is ap- 
proximately 32 degrees, and for a 
monthly mean temperature of 41 
degrees, the mean of the mini- 
mum daily temperatures is ap- 
proximately 32 degrees. 

About 30 per cent of the pre- 
cipitation occurs as snow when 
the monthly mean temperature is 
40 degrees, and practically all of 
it occurs as snow when the mean 
temperature is below 20 degrees. 

Ice Storms. — The surface air 
temperature, however, is not al- 
ways an indication of the char- 
acter of precipitation. In New 
England, New York, Pennsylva- 
nia, and in the states north of 
the Ohio River, in particular, 
rain occasionally falls when the surface air temperature is below 
freezing. The result is an ice storm. In one New England ice 
storm, rain fell when the surface air temperature was 23 degrees 
below freezing.* 

While the picture presented by an ice-coated out-of-doors is 
truly wonderful, the destruction wrought to telegraph, telephone 
and power-transmission wires and to trees is often severe as 
is well illustrated in Fig. 62. f 

* Ice Storms of New England by Chas. F. Brooks, Cambridge, 1914. 
t Variations in Precipitation as Affecting Waterworks Engineering, by 
Carl P. Birkinbine, Am. W. W. Assoc, Vol. 3, No. 1, March, 1916. 



• o 80 
100 



g,*50 

2ft 



t£_ 

-2.- 20 

=510 

££60 
~=80 

S, ioo 

































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Rain 








/C : 


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-/'■"■;, 



J? tit a, -^ > v 

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Fig. 61. — Mean Temperatures and 
Character of Precipitation. 



ELEMENTS OF HYDROLOGY 



Birkinbine states that of 211 storms, 42.5 per cent showed a 
sleet thickness of less than one-quarter inch; 29.4 per cent showed 
a thickness of from one-quarter to one-half inch; 19.9 per cent 
from one-half to one inch; and 8.1 per cent showed an ice coat- 
ing of more than one inch. 




Fig. 62. — Results of an Ice Storm. 

Ice storms are usually very local in character and cannot be 
predicted with any great certainty. They appear to be most 
prevalent in the regions of moderate winter temperature and 
heavy winter precipitation. The essential to the formation 
of an ice storm is a stratum of air with temperature above 
freezing overlying a stratum of air near the earth's surface 
whose temperature is below freezing. Usually the temperature 
of objects on the earth's surface is also below freezing. 

Variation of Precipitation with Latitude, Altitude, etc. — In 
general, precipitation is greatest at the equator and becomes 
gradually less towards the poles. In the regions of the tropics 
of Cancer and Capricorn the precipitation is less than on either 



PRECIPITATION 89 

side of this region, on account of downward air currents, as 
previously explained. 

Precipitation appears to increase with altitude up to about 
3000 feet and then to decrease, although this does not hold 
for mountain regions where the winds are off the ocean. 
Wherever the air currents are off the ocean and upward 
motion is induced by the elevation of the land, precipitation 
increases with altitude to greater elevations than 3000 feet. 

Regions near the ocean may have high or low precipitation, 
depending almost entirely upon whether the winds are off the 
ocean or off the land. 

Irregular Occurrence in United States. — In the region of 
cyclonic precipitation which covers practically all of the United 
States east of the Rocky Mountains, great variations in rain- 
fall are usual occurrences. On the whole, the greater the depth 
of precipitation in the path of the storm the smaller the area 
over which the precipitation extends. 

A good conception of the irregular manner in which precip- 
itation occurs can be secured from a study of Figs. 63 to 66 
showing monthly precipitation in the United States for July, 
August and September, 1915. Were these maps prepared 
on a larger scale, still greater irregularities would be shown. 
Regions that have little rain one month, have considerable 
the next and vice versa. 

For example, in July, the precipitation in southeastern Iowa 
was about 10 inches, in August it was less than 2 inches and in 
September it was between 6 and 8 inches. The region about 
St. Louis had between 6 and 8 inches of rain in July, over 10 
inches in August and less than 2 inches in September. In 
August the precipitation varied from less than 2 inches at 
Keokuk, Iowa, to over 10 inches at St. Louis, Mo., about 150 
miles distant, and from over 15 inches in southwestern Arkansas 
to less than 4 inches in the southeastern part of the same state. 
Other irregularities, equally great, are to be found elsewhere 
in the United States and in almost any month of any year. 



90 



ELEMENTS OF HYDROLOGY 



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PRECIPITATION 



91 




92 



ELEMENTS OF HYDROLOGY 





1PITATI0N 

inches 



Pfepared by Henry Gannett 
mainly from data of the 
United States Geological Survey 
and United States Weather Bureau 




Courtesy U. S. Geological Survey. 



MAP OF UNITED STATES, SHOWING MEAN ANNUAL PRECIPITATION 

Red lines and figures indicate average annual precipitation in depth in inches 



Ptepared by Henry Ganm 
nainly from data of the 
Jnited States Geological Syr 
nd United States Weather B 



Fig. 67. 



PRECIPITATION 



93 




Sept ember 
Fig. 66. — Profile along 35th Parallel showing Irregularity of Precipitation 
during July, August and September, 1915. 

Mean Annual Precipitation. — The mean annual precipitation 
in the United States is shown in Fig. 67. As longer records 
become available, these averages may be changed somewhat. 
The annual precipitation at any given station varies consid- 
erably from year to year. Binnie * concluded that a thirty- 
year-mean would probably be in error about 2 per cent; a 
twenty-year mean 3| per cent; a ten-year mean 8| per cent; 
and a five-year mean might be in error 15 per cent. 

Records of mean annual precipitation are not of much service, 
however, in the design of most works for the utilization or 
control of water. The runoff resulting from the average pre- 
cipitation can seldom be utilized. Records of exceptionable 
conditions are of more importance, on the whole, than records 
of average conditions. 

Cycles in Annual Precipitation. — Graphs of annual and 

progressive mean annual precipitation together with frequency 

* Binnie, Sir Alexander, Rainfall, Reservoirs, and Water Supply, 1913, 
p. 10. 



94 



ELEMENTS OF HYDROLOGY 



curves of annual precipitation at a number of long-term stations 
in the United States are shown in Figs. 68 to 105. 



CO 



~ 50 



id 



:;d 



;ii. 




ANNUAL PRECIPITATION 

AT 

NEW BEDFORD, MASSACHUSETTS 

During period of 101 years 



Fig. 68. 




10 



ANNUAL PRECIPITATION 

AT 

BOSTON, MASS. 

During Period of 97 Years 



Fig. 69. 



60 



S50 



I 

d 
.2 10 



£30 



20 



10 




ANNUAL PRECIPITATION 

AT 

PROVIDENCE, RHODE ISLAND 

During Period of 83 Years 



Fig. 70. 



Average Annual Precipitation : 
Boston, | Mass. 

\New Bedford, " 



ProvidencelR.l 



9 50 - 



30 



< 20 




ANNUAL PRECIFITATION 

IN 

NEW ENGLAND STATES 

During Period of 83 Years 



Fig. 71. 



(95) 



96 



ELEMENTS OF HYDROLOGY 



GO 



50 



S 40 



:jo 




ANNUAL PRECIPITATION 

AT 

CINCINNATI, OHIO 

During Period of 80 Years 



8 3 



Fig. 72. 



BO 



50 



a 30 | 



S20- 




ANNUAL PRECIPITATION 

AT 

PORTSMOUTH, OHfO 

During Period of 82 Years 



Fig. 73. 



PRECIPITATION 



97 



60 



50 



o40 



30- 



-i SO- 



10 




ANNUAL PRECIPITATION 

AT 

MARIETTA, OHIO 

During Period of 93 Years 



0000 



Fig. 74. 



60 



50 



£40 



-2 

•S.30 



S20 

c 
a 
< 



10 




ANNUAL PRECIPITATION 

IN 

UPPER OHIO RIVER VALLEY 

During Period of 80 Years 



Fig. 75. 



98 



ELEMENTS OF HYDROLOGY 



TO- 



GO 



50- 



40 



■i0 



30 



10 




ANNUAL PRECIPITATION 

AT 

WASHINGTON, D.C. 
During Period of 63 Years 



Fig. 76. 



PRECIPITATION 



99 




Fig. 77. 



100 



ELEMENTS OF HYDROLOGY 



'■M 



CO 



.2 50- 



fk 40- 



30 



20 



10 




ANNUAL PRECIPITATION 

AT 

NEW ORLEANS, LOUISIANA 

During Period of 67 Years 



o ■* 



Fig. 78. 



PRECIPITATION 



101 



70 



60 



50 



40 



30 



20 



10 




ANNUAL PRECIPITATION 

AT 

SAINT LOUIS, MISSOURI 

During Period of 78 Years 



Fig. 79. 




Fig. 80. 



102 



ELEMENTS OF HYDROLOGY 



tor 



ANNUAL PRECIPITATION 

AT 

HAVRE, MONTANA 

During Period of 35 Years 




Fig. 81. 



30 



■JO 



<M0 




ANNUAL PRECIPITATION 

AT 
SALT LAKE CITY, UTAH 
During Period of 10 Years 



Fig. 82. 



30 



ANNUAL PRECIPITATION 

AT 

EL PASO, TEXAS 

During Period of 36 Yoars 




Fig. 83. 




Fig. 85. 



(103) 



104 



ELEMENTS OF HYDROLOGY 




Fig. 86. 



PRECIPITATION 

70 



105 






































FREQUENCY OF 

ANNUAL PRECIPITATION 

AT 

BOSTON. MASS. 

1818-19H 





















25 50 75 100 

;Per cent of Total Time (101 years) 

Fig. 87. 



25 50 75 100 

Per cent of Total Time (97 years) 

Fig. 88. 



60 



S? 50 



o 10 



jF 30 



< 20 



10 





. 


— — — —— 






























■FREQUENCY OF 

ANNUAL PRECIPITATIOr 

AT 

PROVIDENCE.-R.I. 

18S2-19H 


< 



















60 



10 



30 



g 20 

a 





























FREQUENCY OF 
ANNUAL PRECIPITATION 

IN 

NEW ENGLAND STATES 

1832-1914 

AVERAGE OF 

BOSTON, MASS. 

NEW BEDFORD, MASS. 

PROVIDENCE, R.I. 

















25 50 75 100 

Per cent of Total Time (83 years) 

Fig. 89. 



25 50 75 100 

Per cent of Total Time (83 years) 

Fig. 90. 



106 



ELEMENTS OF HYDROLOGY 



50 



.2 10 



& 30 



B 
-< 20 



10 













































FREQUENCY OF 

ANNUAL PRECIPITATION 

AT 

CINCINNATI, OHIO 

1835-1914 













25 50 75 100 

Per cent of Total Time (80 years) 

Fig. 91. 



50 

SI 

o 40 


















a 












a 
o 

§S0 












a. 

"5 

o 

h 

ft 












a 
g20 

c 














FREQUENCY OF 
ANNUAL PRECIPITATION 








AT 
PORTSMOUTH, OHIO. 




10 





1830-1914 














1 


25 50 75 


100 



7fl 



(id 



50 



S40 













































FREQUENCY OF 

ANNUAL PRECIPITATION 

AT 

MARIETTA, OHIO, 

1818-1914 













50 



30 



20 



Per cent of Total Time (82 years) 

Fig. 92. 





























FREQUENCY OF 

ANNUAL PRECIPITATION 

IN 

UPPER OHIO RIVER VALLEY 

1835-1914 

AVERAGE OF 

MARIETTA, OHIO. 

PORTSMOUTH, OHIO. 

CINCINNATI, OHIO. 

















25 50 75 

Per cent of Total Time (93 years) 

Fig. 93. 



100 



25 50 75 

Per cent of Total Time (80 years) 

Fig. 94. 



100 





































FREQUENCY OF 

ANNUAL PRECIPITATION 

AT 

WASHINGTON, D.C. 

1852-1911 























•-! 


5 5 


1 7 


r > 


100 



Per cent of Total Time (63 years) 

Fig. 95. 





















































FREQUENCY OF 

ANNUAL PRECIPITATION 

AT 

NEW ORLEANS, LA. 

1839-1914 





















60 



c 50 



S 40 



30 













































FREQUENCY OF 

ANNUAL PRECIPITATION 

AT 

SAVANNAH, GA. 

1840-1911 






















60 



50 



25 50 75 100 

Per cent of Total Time (63 years) 

Fig. 96. 





































FREQUENCY OF 

ANNUAL PRECIPITATION 

AT 

ST. LOUIS, MISSOURI. 

1837-1914 





















25 50 75 

Per cent of Total Time (67 years) 

Fig. 97. 



25 50 75 100 

Per cent of Total Time (78 years) 



Fig. 98. 



(107) 



108 

50 
40 



ELEMENTS OF HYDROLOGY 



K 20 





























FREQUENCY OF 

ANNUAL PRECIPITATION 

AT 

ST.PAUL, MINNESOTA 

1837-1915 













25 50 75 

Per cent of Total Time (79 years) 

Fig. 99. 



30 



20 





FREQUENCY OF 

ANNUAL PRECIPITATION 

AT 

HAVRE, MONTANA 

1880-1914 





















25 50 75 100 

Per cent of Total Time (35 years) 

Fig. 100. 



-10 





FREQUENCY OF 
ANNUAL PRECIPITATION 

AT 

SALT LAKE CITY, UTAH 

1875-1911 



















25 50 75 100 

Per cent of Total Time (40 years) 

Fig. 101. 



, 30 



S20 





FREQUENCY OF 

ANNUAL PRECIPITATION 

AT 

EL PASO, TEXAS 

1879-1914 

























5 5 


) T 


5 


100 



Per cent of Total Time (36 years) 

Fig. 102. 



20 





FREQUENCY OF 

ANNUAL PRECIPITATION 

AT 

SAN DIEGO, CAL. 

1850-1914 





















25 50 75 

Per cent of Total Time (65 years) 

Fig. 103. 



40 



J2 

a 30 



20 





























FREQUENCY OF 
ANNUAL PRECIPITATION 

AT 

SAN FRANCISCO, CAL. 

1850-1914 





25 50 75 100 

Per cent of Total Time (65 years) 

Fig. 104. 



PRECIPITATION 



109 



no 



100 



90 



K0 



70 



60 



50 



30 



20 





























































FREQUENCY OF 

ANNUAL PRECIPITATION 

AT 

ASTORIA, OREGON 

1854-1914 





























25 50 75 100 

Per cent of Total Time (61 years) 



Fig. 105. 



110 ELEMENTS OF HYDROLOGY 

While attention has been called to the occurrence of nat- 
ural phenomena in cycles, a study of variations in annual rain- 
fall in the United States tends to indicate a lack of correlation 
between solar phenomena and precipitation. 

If high and low annual precipitation occurred in synchro- 
nism with sun spots, one would expect to find the extremes 
of precipitation occurring simultaneously over large areas, at 
least, yet the graphs for Boston, New Bedford and Providence 
stations which are relatively close together show most strik- 
ing divergence from the expected correspondence. The same 
conclusion holds with respect to the three Ohio River stations, 
Marietta, Portsmouth and Cincinnati. 

A study of the graphs of Figs. 68 to 86 shows cycles of such 
irregular length, magnitude and diversity with respect to time 
as to lead one to believe that the amount of annual precipitation 
at any given observation station is a chance occurrence rather 
than the effect of a regularly- varying cause.* 

Relation Between Length of Record and Extremes of Annual 
Precipitation. — Efforts to show a relation between length 
of record and maximum and minimum annual precipitation 
lead to erroneous conclusions. In general, it is, of course, true 
that the longer the term of years over which records extend, 
the higher the maximum and the lower the minimum. Excep- 
tions, however, are about as frequent as the rule. This is 
well illustrated by the records for St. Paul, Minn., Cincinnati, 
Ohio, New Bedford, and Boston, Mass., graphically presented 
in Fig. 106. The recorded maximum annual precipitation at 
St. Paul, for example, occurred in the 13th year of the record 
and the minimum occurred in the 74th year of the record. 
Moreover, the 74th year minimum was only about two thirds 
of the minimum for the preceding 73 years. At St. Paul, New 
Bedford and Cincinnati, the maximum occurred near the begin- 
ning of the record. At Boston it occurred near the middle. 
At St. Paul and Cincinnati the minimum occurred near the 

* Secular Variation of Precipitation discussed by A. J. Henry in Bulletin 
D, Weather Bureau, 1897, p. 18. 



PRECIPITATION 



111 



end of the record. At New Bedford and Boston it occurred 
near the beginning. 



45 



£ 40 
o 35 



£■ 30 
o 

£25 

20 

15 

10 

5 

























































Maximum 


/ 




*" Maiimun 

1 1 








\ 
Maximum 
























ANNUAL PRECIPITATION 

AT 
NEW BEDFORD, MASS- 






ANNUAL 

PRECIPITATION 

AT 

CINCINNATI, OHIO 










































r 


_r 




| 








^Me 


an 






V J 






1 


Maximum 

1 


/ 










IT 










I 










ANNUAL 

PRECIPITATION 

AT 

ST. PAUL. 

MINNESOTA 


1 




/>- Mean 

1 




"""L 


ZL 


,^-Wi 


uiniui 


1 


I 










iT 




ANNUAL 
PRECIPITATION. 

AT 
BOSTON, MASS. 












_j£ 


- Mini 


quid 


































J 




Meal 


I 






V.- • 1 
^-Minimum 








































































n 


Mil 


limun 


> 






















































LACK QF RELATION BETWEEN LENGTH OF RECORD 

AND 
MAXIMUM AND MINIMUM ANNUAL PRECIPITATION 
























Ill 



20 40 60 80 
Years Record 



20 40 60 
Years Record 



20 40 60 
Years Record 



20 40 60 80 100 
Years Record 



Fig. 106. 



Map of Probable Extremes of Annual Precipitation in United 
States. — In view of this lack of relation between length of 
record and probable maximum and minimum annual precipi- 
tation in different regions, the author made a study of all the 
records of annual precipitation available for the United States 
up to and including the year 1914. The maximum and the 
minimum for each station were selected, and with these as a 
basis, maps of probable maximum and minimum annual pre- 
cipitation, Fig's. 107 and 108, were prepared. The extremes 
in any given locality were given most weight and isolated records 
that clearly conflicted with these were disregarded. While 
the records in no case extend over a longer period than 101 
years, it is probable that the limits of annual rainfall indicated 
on this map will not be exceeded at any one station in the eastern 
half of the United States with a greater frequency than once 
in several hundred years. 



112 



ELEMENTS OF HYDROLOGY 




PRECIPITATION 



113 



S -£ <*> oj 




114 



ELEMENTS OF HYDROLOGY 



Monthly Precipitation. — The shorter the unit of time, the 
greater the diversity in amount of precipitation which may 
be expected in the given time. The curves of Figs. 109 to 120 
show the maximum, minimum and mean monthly precipitation; 
the precipitation for each month of the wettest year and of 
the driest year, together with frequency curves of monthly 





M J J Ai S N D 10 20 30 40 50 60 70 80 90 100 
Months Frequency —Per cent of Total Mouths 

Fig. 109. — Monthly Precipitation at New Bedford, Mass. Records of 101 

years. 

precipitation, at typical stations in the United States, based 
on the records of the U. S. Weather Bureau, to 1914 incl. The 
average monthly precipitation has been added to the frequency 
curve, and it is interesting to note that the monthly precipitation 
is above the average for about 40 per cent of the time and 
below the average for about 60 per cent of the time. This 
fact raises the question of whether the use of the average pre- 
cipitation as the " normal " is justifiable. 








































































































































































































































































F~" 










lAverage Monthly 
Precipitation 























































A M J J A 
Months 



10 20 30 40 50 60 70 80 90 100 
Frequency -Per cent of Total Months 



Fig. 110. — Monthly Precipitation at Washington, D. C. Records of 77 years. 
































































































































































































































































































































































































\\ ei 


age 


Hon 


M^ 














Pr 


scipi 


tati< 


J 











































































M J J A 
Months 



10 20 30 40 50 60 70 80 90 100 
Frequency — Fer oent of Total Months 



Fig. 111. — Monthly Precipitation at Savannah, Georgia. Records of 66 years. 

(115) 



24 

23 

22 

21 

20 

19 

18 

17 

tS 16 
a 
| 15 

3 14 

ft 

8 18 

A 

§12 

In 

O 

5 10 









































II 
























/I 
























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im s 


1 J 


















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1 




















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tost 


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187 








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k Avt 


rage Moi 


tl.ly 




V 


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itati 


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10 20 30 40 50 60 70 80 90 100 
Frequency— Per cent- of Total Months 



M J J A 
Months 

Fig. 112. — Monthly Precipitation at New Orleans, La. Records of 70 years. 

18 
17 

16 


























































































































































































































































































































Av 


-'ree 


• Mo 
pita 


nth! 

ion 


y 





















































M J J A S ON D 10 20 30 40 50 60 70 80 90 100 
Months Frequency - Per cent of Total Months 

Fig. 113. — Monthly Precipitation at St. Louis, Mo. Records of 79 years. 

(116) 



PRECIPITATION 



117 










































































































































































































I 








Average Monthly 
Precipitation 

































M J J A 
Months 



10 20 30 40 50 60 70 80 90 100 
Frequency - Per cent of Total Months 



Fig. 114. — Monthly Precipitation at St. Paul, Minn. Records of 79 years. 
















































































































































































_J 






Average 
Precipi 


Monthly 
tation 















M J J A 
Months 



10 20 30 40 50 60 70 80 90 100 
Frequency - Per cent of Total.Months 



Fig. 115. — Monthly Precipitation at Havre, Montana. Records of 36 years. 


















































































































Arenge Monthly 


Preoipitati 
1 













10 20 30 40 50 60 70 80 90 100 
Frequency — Per cent of Total Months 

Monthly Precipitation at Salt Lake City, Utah. Records of 42 

years. 



118 



ELEMENTS OF HYDROLOGY 










• 











































































































































































































10 20 30 40 50 60 70 80 90 100 
Frequency— Per cent of Total Months 



Fig. 117. — Monthly Precipitation at El Paso, Texas. Records of 53 years. 



M » 
I 

l 4 

-2 3 

a 

t 2 

o 
u 

* 1 






























^ 


nxiir 


ura 
















J 




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r 






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i 


f 


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Wet 

Year- 


e3t \\ 














/ 


A 




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i 




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in 


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4 
/ 


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s 


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V 


Driest Years 


<< 


r7 





F M A M 



J J A S O N 
Months 



















































































































































































































— J 


_J 





) 10 20 30 40 50 60 70 80 90 100 
Frequency Per cent of Total Months 



Fig. 118. — Monthly Precipitation at San Diego, Calif. Records of 86 years. 



PRECIPITATION 



119 



26 



S16 



St* 

o 

£13 
I 
§12 

| 11 

Sf io 



7 
6 
5 
4 
3 
2 
1 


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1 




















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1 




















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\ / 


A 


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imm 


a 






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/ 












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A 








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1 








, 


f 




A 


w 


fttest Ye 
1884 


i -\ 


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/ 
















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7 






-M. 


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Driest YearV 
1898 > 






X 




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-n 




saV 


A 


k 


/ 








A** 


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/ 




. 


V 


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Aver 
—Pi 


age 


Horn 

tati( 


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M J .1 A 
Months 



5 
4 
3 

g 

1 

10 20 30 40 50 60 70 80 90 100 
Frequency -Per cent of Total Months 

Records of 66 



119. — Monthly Precipitation at San Francisco, Cal. 

years. 



120 



ELEMENTS OF HYDROLOGY 



27 
26 
25 
24 
23 
22 
21 
SO 

al9 

o 

Sl8 

Il7 
w 

.§16 

o 

m!5 

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Ii3 

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11 



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f 














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1 


















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1 -& 







J F M A M 



J J A 
Months 



S O N D 











































































































































































































































































































































































































































































Ave. 


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10 20 30 40 50 60 70 80 90 100 
Frequency— Per cent of Total Months 



Fig. 120. — Monthly Precipitation at Astoria, Oregon. Records of 62 years. 



PRECIPITATION 121 

Webster's International Dictionary defines " normal " as the 
"ordinary or usual condition, degree, quantity or the like; 
average; mean." . It is apparent that the average or mean 
monthly precipitation is not, by any means, " the ordinary 
or usual " monthly rainfall. The difficulty with the application 
of this definition lies in the fact that identical recurrences of 
natural phenomena are extemely rare. However, the amount 
of precipitation which occurs most frequently in any given 
period of time would appear to best meet the condition imposed 
by the definition. 

It would seem that the normal condition is that which pre- 
vails the greatest portion of the time, whether the phenomena 
be annual, monthly or daily precipitation, or lake or river stage. 
The "normal," according to this definition, can usually be readily 
determined from the frequency curve by noting the point of 
inflection. On some of the curves the change of curvature is 
so gradual, however, that the point of inflection cannot readily 
be ascertained. 

If more than one half the total number of months over which 
records extend, have no rainfall, for example, then the nor- 
mal condition is zero monthly rainfall, though the average may 
still be one or two inches or more. The normal rainfall during 
months when any rainfall occurs would, of course, be a quantity 
of some magnitude. 

Determination of True Monthly Mean. — A map of the great- 
est recorded monthly rainfall in Minnesota is shown ui Fig. 121. 
A variation in rainfall from less than 2 inches in the northwest 
corner of the State, to more than 14 inches in the southeast 
corner, will be noted, notwithstanding the generally heavy pre- 
cipitation over the whole State. 

When an accurate mean rainfall over an area such as the State 
of Minnesota is desired, it is necessary to determine the average 
precipitation from an isohyetal map such as Fig. 121. The 
mean derived from a simple average of the observed quanti- 
ties at the different stations, as published by the Weather 



122 



ELEMENTS OF HYDROLOGY 



Bureau, gives 8.34 inches. By determining the true mean 
from the map, the low precipitation over the northeastern 
part of the State, in which relatively few observation stations 
are located, receives its proper weight and the mean is reduced 
to 7.57 inches. 




RAINFALL MAP OF MINNESOTA 

SHOWING 

ISOHYETALS FOR JUNE, 1914 



Fig. 121. 



Excessive Monthly and Daily Precipitation. — Fig. 122 is 
a summary of the results of a study of the records of daily 
and monthly precipitation in Minnesota, Ohio, Kansas and Ala- 
bama. The frequency of occurrence of both daily and monthly 



PRECIPITATION 



123 



precipitation was worked up on large-scale logarithmic cross- 
section paper, and merely a summary of the results is presented. 
The base data, upon which the conclusions of Fig. 122 are based, 
are summarized in Tables 4 and 5. As the number of stations 
per unit area varied somewhat in the different states, the data 
were reduced to the basis of one rainfall station for each 500 
square miles. For example, in eastern Kansas, there was one 



DAILY PRECIPITATION 

EXCEEDED WITH GIVEN FREQUENCY 

IN MISSISSIPPI VALLEY 

Y7%\ Once in 100 Years 
ra<3 Once in 25 Years ' 

SB Once in 10 Years 
Data Reduced to Basis of 
One Rainfall Station for every 500 S<J. Miles 



MONTHLY PRECIPITATION 
Alabama EXCEEDED WITH GIVEN 

frequency- 





Fig. 122. 



station for each 643 square miles. The number of recorded 
daily rainfalls of all magnitudes in this section of the State was 
increased in the ratio of 643 to 500 for the purpose of reducing 
the observed precipitation to the equivalent of one rainfall 
station for every 500 square miles. The states selected are be- 
lieved to be typical of the larger portion of the United States 
east of the Rocky Mountains and to afford as satisfactory a 
basis for estimating the amount of rain which may be ex- 
pected to fall in a day and in a month in these regions as 
present records furnish. 



124 



ELEMENTS OF HYDROLOGY 



TABLE 4. — RECORDS OF EXCESSIVE DAILY PRECIPITATION 

State of Minnesota 

72 stations — 1180 square miles per station 







Number of days with given daily precipitation - 


- inches depth 




Total 
days 


Year 


1.00 
to 
1.24 


1.25 
to 
1.49 


1.50 
to 
1.74 


1.75 
to 
1.99 


2.00 

to 
2.49 


2.50 

to 

2.99 


3.00 
to 
3.99 


4.00 

to 

4.99 


5.00 
to 
5.99 


6.00 
to 
6.99 


7.00 
to 

7.99 


8.00 

to 

8.99 


9.00 

to 

9.99 


10.00 

to 
10.99 


*1895 


89 


42 


35 


19 


31 


11 


13 


3 








1 











244 


1896 


162 


69 


57 


35 


43 


15 


15 


3 





1 














400 


1897 


123 


51 


46 


20 


29 


18 


18 


3 


1 

















309 


1898 


102 


63 


39 


23 


29 


8 


10 


1 








1 











276 


1899 


139 


86 


50 


37 


50 


20 


17 


4 


2 








1 








406 


1900 


162 


81 


60 


41 


52 


26 


21 


13 


2 

















458 


1901 


124 


63 


46 


31 


34 


17 


13 


1 


1 


1 














331 


1902 


138 


69 


61 


41 


44 


12 


10 


5 


1 

















381 


1903 


173 


89 


71 


30 


50 


21 


16 


10 


1 

















461 


1904 


123 


66 


39 


20 


31 


10 


3 


1 




















293 


1905 


202 


102 


64 


47 


62 


10 


14 























501 


1906 


157 


75 


63 


28 


40 


9 


10 


3 





1 














386 


1907 


127 


62 


44 


43 


46 


15 


7 


1 





2 














347 


1908 


199 


107 


109 


47 


36 


10 


8 


5 


2 

















525 


1909 


173 


89 


51 


33 


44 


17 


17 


3 

















2 


427 


1910 


83 


33 


14 


5 


9 


5 


1 























150 


1911 


150 


82 


59 


30 


40 


21 


12 


2 





1 














397 


1912 


130 


65 


40 


28 


20 


8 


6 


3 








1 











301 


1913 


147 


113 


62 


37 


33 


11 


9 


1 











1 








414 


1914 


220 


116 


93 


41 


47 


16 


18 


3 


1 

















555 


1915 


180 


102 


79 


38 


39 


17 


7 


1 




















463 


Total 


3103 


1625 


1182 


674 


809 


297 


245 


66 


11 


6 


3 


2 





2 


8025 


Cum. total 


8025 


4922 


3297 


2115 


1441 


632 


335 


90 


24 


13 


7 


4 


2 


2 










Once in gb 


fen m 


imber 


of ye 


ars 












Frequency 


0.08 


0.13 JO 19 |0.30 


0.44 ll 00 


>., 


7.0 


26.3 


49 


91 


159 


312 


312 





100 stations 



State of Ohio 

410 square miles per station 





Number of day 


s with 


given daily precipitation — 


inches depth 




Total 
days 


Year 


1.00 
to 
1.24 


1.25 

to 
1.49 


1.50 
to 
1.74 


1.75 
to 
1.99 


2.00 
to 

2.49 


2.50 

to 

2.99 


3.00 

to 

3.99 


4.00 

to 

4.99 


5 00 

to 

5.99 


6 00 

to 

6.99 


7.00 
to 
7.99 


1900 


312 


111 


68 


20 


35 


9" 


5 














560 


1901 


235 


139 


89 


54 


46 


17 


10 


3 











593 


1902 


289 


157 


83 


58 


48 


16 


7 


3 











661 


1903 


357 


153 


75 


38 


44 


18 


6 


2 


1 


1 





695 


1904 


308 


162 


93 


48 


39 


19 


8 


1 





1 





679 


1905 


354 


173 


124 


53 


69 


22 


11 


3 


1 








810 


1906 


289 


113 


63 


38 


44 


17 


2 














566 


1907 


409 


188 


94 


63 


57 


16 


8 


4 











839 


1908 


290 


147 


71 


33 


27 


14 


3 


1 











586 


1909 


351 


177 


131 


58 


53 


9 


14 


5 


1 








799 


1910 


305 


126 


75 


34 


63 


24 


19 


1 








1 


648 


1911 


291 


156 


92 


53 


59 


23 


22 


3 











699 


1912 


303 


149 


75 


45 


66 


21 


15 


2 











676 


1913 


337 


159 


97 


77 


109 


46 


34 


11 


2 


2 


1 


875 


1914 


356 


184 


107 


49 


53 


9 


14 











1 


773 


Total 


4,786 


2294 


1337 


721 


812 


280 


178 


39 


5 


4 


3 


10,459 


Cum. total 


10,459 


5673 


3379 


2042 


1321 


509 


229 


51 


12 


7 


3 












Once i 


n givei 


l number of j 


ears 










Frequency 


0.17 


0.32 


0.54 


0.89 


1.39 


3.57 | 8.0 


35.7 


151 


263 


610 





* April-December incl. 



PRECIPITATION 



125 



TABLE 4. — RECORDS OF EXCESSIVE DAILY 

PRECIPITATION — (Continued) 

State of Kansas (eastern section) 

42 stations — 643 square miles per station 







Number of days with given daily precipitation 


— inches depth 


Total 
days 


Year 


1.00 
to 
1.24 


1.25 
to 
1.49 


1 50 
to 
1.74 


1.75 

to 
1.99 


2.00 

to 

2.49 


2.50 

to 

2.99 


3.00 

to 

3.99 


4.00 

to 

4.99 


5.00 

to 

5.99 


6.00 

to 

6.99 


7.00 
to 
7.99 


8.00 
to 

8.99 


9.00 
to 

9.99 


1900 


109 
76 
128 
164 
129 
102 
97 
134 
173 
163 
129 
92 
122 
131 
149 

1898 
5509 


59 
37 
81 
72 
71 
69 
57 
82 
103 
64 
67 
51 
90 
81 
78 

1062 
3611 


54 
37 
56 
72 
53 
42 
42 
60 
78 
62 
55 
51 
55 
55 
50 

822 

2549 


32 
13 
40 
30 
36 
25 
18 
23 
37 
42 
29 
39 
50 
34 
45 

493 

1727 


46 

22 
58 
42 
61 
45 
25 
28 
65 
59 
39 
29 
51 
31 
39 

640 
1234 


17 

5 

23 
22 
23 
29 
11 
17 
35 
26 

9 
14 
15 
16 
21 

283 
594 


16 
2 
10 
12 
25 
16 
12 
5 
28 
22 
8 
13 
15 

8 
21 

213 
311 


3 


2 
8 
4 
5 
8 
3 
5 
9 
2 
3 
2 
1 
2 

57 
98 


4 




2 
2 
3 
1 
4 
4 

2 

1 
1 
3 

27 
41 







1 
1 
1 
1 

1 




2 

1 

8 
14 








1 


3 

1 



1 

6 
6 






340 


1901 






192 


1902 






398 


1903 






422 


1904 






405 


1905 






336 


1906 






275 


1907 






354 


1908 






529 


1909 






454 


1910 






338 


1911 






295 


1912 






403 


1913 






358 


1914 






410 


Total 






5509 


















Once in given 


number of years 








Frequency 


0.09 


0.13 


0.19 


0.28 1 


0.40 


0.83 


1.6 | 


5.0 1 


12.0 I 


35 1 


82 1 


i 

1 







State of Kansas (western section) 
26 stations — 1040 square miles per station 





Number of days with given daily precipitation — inches depth 


Total 
days 


Year 


1.00 
to 
1.24 


1.25 

to 
1.49 


1.50 
to 

1.74 


1.75 
to 
1.99 


2.00 
to 

2 49 


2.50 
to 
2.99 


3.00 

to 

3.99 


4.00 

to 

4.99 


5.00 

to 

5.99 


6.00 
to 
6.99 


7.00 
to 
7.99 


8.00 

to 

8.99 


9.00 

to 

9.99 


1900 


24 
28 
38 
37 
45 
43 
54 
41 
50 
39 
17 
33 
56 
44 
51 

600 
1575 


16 
11 
28 
14 
21 
20 
26 
18 
24 
32 
11 
19 
46 
17 
33 

336 
975 


12 
14 
24 
10 
17 
17 
22 
11 
13 
17 
7 
5 
35 
19 
25 

248 
639 


7 
5 

10 
7 
8 

12 
9 
5 
8 

12 
1 
4 

13 
6 

17 

124 
391 


11 
5 
16 

7 

7 

15 

12 

7 

8 

12 

6 

11 

18 

8 

13 

156 
267 


1 

3 
6 

2 
3 
2 
3 
2 
1 
3 
3 
9 
3 
8 

49 
111 


4 

2 
4 
1 
3 

3 
3 
5 
1 
1 
3 
1 
5 

36 
62 



1 
2 
3 

1 

1 
4 
1 
1 

1 
1 
2 

18 
26 


1 


1 
1 



1 









1 

5 

8 







1 






1 





2 
3 




1 














1 
1 






76 


1901 






68 


1902 






127 


1903 






83 


1904 






101 


1905 






115 


1906 






126 


1907 






89 


1908 






112 


1909 






119 


1910 






47 


1911 






77 


1912 






181 


1913 






99 


1914 






155 


Total 






1575 
























Once in given number of years 




Frequency 


0.12 0.19 10 29 10.48 10.70 1 1 . 70 1 3.0 1 7.2 123.4 162.5 1 188 


1 


























1 





126 



ELEMENTS OF HYDROLOGY 



TABLE 4. — RECORDS OF EXCESSIVE DAILY 

PRECIPITATION — (Concluded) 

State of Kansas (middle section) 

38 stations — 710 square miles per station 





Number of day 


s with 


given daily precipitation — 


inches depth 


Total 
days 


Year 


1 00 
to 
1.24 


1.25 

to 
1.49 


1.50 
to 
1.74 


1.75 

to 
1.99 


2.00 
to 
2.49 


2.50 

to 

2.99 


3.00 

to 

3.99 

2 

2 

12 
13 

4 
13 

4 

7 
18 

8 

7 

8 

7 

2 

3 

110 
153 


4 00 

to 

4.99 

2 

3 
2 
3 
5 
2 
1 
3 
4 

2 
4 
1 
1 

33 
43 


5.00 
to 

5.99 

1 


1 
1 


3 





2 



8 
10 


6.00 
to 
6.99 


7 00 
to 
7.99 






1 










1 
1 


8.00 

to 

8.99 


9.00 

to 

9.99 


1900 


79 
62 
86 
89 

104 
92 
80 
90 

114 

103 
76 
98 

123 
89 
67 

1352 
3685 


36 
35 

54 
58 
66 
59 
48 
43 
70 
54 
33 
57 
58 
50 
53 

774 
2333 


25 
12 
49 
39 
41 
41 
42 
35 
55 
39 
22 
33 
47 
32 
20 

532 
1559 


20 
6 
24 
23 
24 
22 
19 
26 
32 
26 
11 
30 
19 
23 
23 

328 
1027 


26 
6 
30 
45 
25 
39 
19 
21 
34 
42 
17 
16 
35 
15 
17 

387 
699 


9 

6 
11 
18 
12 
7 
10 
9 
18 
23 
10 
6 
8 
4 
8 

159 
312 








1 









1 

2 






200 


1901 






129 


1902 






270 


1903 






288 


1904 






279 


190f> 






279 


1906 






228 


1907 






232 


1908 






344 


1909 






299 


1910 






176 


1911 






250 


1912 






303 


1913 






216 


1914 






192 


Total 






3685 


























Once 


n give 


n number of years 








Frequency 


0.11 


0.17 


0.26 


0.39 


0.57 


1.3 |2.6 |9.3 1 40 


200 


400] .... 1 ... . 





State of Alabama 
65 stations — 800 square miles per station 





Number of day 


s with 


given 


iaily precipitation — 


inches depth 




Total 
days 


Year 


1.00 
to 
1.24 


1.25 
to 
1.49 


1.50 
to 
1.74 


1.75 
to 
1.99 


2.00 
to 
2.49 


2.50 

to 

2.99 


3.00 

to 

3.99 


4.00 
to 
4.99 


5.00 
to 

5.99 


6.00 

to 

6.99 


7.00 
to 
7.99 


8.00 

to 

8.99 


9.00 
to 
9.99 


1901 


343 


202 


188 


113 


178 


62 


58 


24 


7 


4 


4 


1 





1,184 


1902 


337 


178 


121 


83 


135 


51 


61 


15 


10 


1 


1 





1 


994 


1903 


340 


186 


158 


86 


141 


42 


48 


13 


6 


2 


1 





1 


1,024 


1904 


324 


175 


103 


73 


66 


12 


13 


6 

















772 


1905 


340 


185 


150 


96 


134 


53 


40 


13 


7 


1 


1 








1,020 


1906 


276 


195 


156 


116 


131 


58 


49 


23 


5 


6 


2 


2 





1,019 


1907 


368 


221 


159 


98 


159 


52 


23 


12 





2 


1 








1,095 


1908 


299 


186 


130 


94 


112 


50 


42 


23 


3 





1 


' 





940 


1909 


358 


245 


200 


120 


161 


55 


59 


22 


3 














1,223 


1910 


275 


188 


128 


63 


87 


28 


18 


5 


4 


1 











797 


1911 


383 


206 


145 


78 


149 


48 


40 


10 


1 


1 





1 





1,062 


1912 


414 


248 


197 


122 


176 


88 


76 


18 


4 


1 








1 


1,345 


1913 


315 


190 


143 


95 


142 


63 


48 


13 


4 


2 





1 





1,016 


1914 


295 


189 


128 


70 


102 


38 


24 


2 


1 














849 


1915 


306 


192 


138 


124 


154 


68 


62 


28 


7 


2 


1 








1,082 


Total 


4,973 


2,986 


2244 


1431 


2027 


768 


661 


227 


62 


23 


12 


5 


3 


15,422 


Cum. total 


15,422 


10,449 


7463 


5219 


3788 


1761 


993 


332 


105 


43 


20 


8 


3 












Once i 


n giver 


1 number of years 












Frequency 


0.04 


0.06 


0.08 


0.12 


0.16 


0.35 |0.6 |l.8 [5.8 


14.1 


30.5 


76 


203 





PRECIPITATION 



127 



TABLE 5. — RECORDS OF EXCESSIVE MONTHLY 
PRECIPITATION 





Precipitation — inches per month 


State of Minnesota, 
1896-1915 incl. 


© ** 

00 


2© 
■* 

10 © 
00 


-2© 
©^ 

W© 

© ^ 


So, 

©■* 


Q 

*^ C 

'"cm 




~© 






"a 


2© 
©"»■ 
















Eastern section, 41 


87 
268 


84 
181 


45 
97 


23 

52 


12 
29 


11 
17 


5 
6 


1 
1 








1160sq. mi. persta., 
Cumulative total 








































Once in given number of years 


Frequency 


1.32 


1.95 


3.6 


6.8J 12 


21 


59 | 500 
































Western section, 32 
stations 


23 

75 


19 

52 


16 
33 


7 
17 


4 
10 


2 
6 


1 

4 


2 
3 


1 
1 
















1160sq. mi. persta., 
Cumulative total 






































Once in given number of years 


Frequency ........ 


3.7 |5.5 |8.3 [I6.2|27.8|46.l| 69 | 92 1 278 j 1 . . . .1. . . .1... .1.. . .1. ...I... . 




Precipitation — inches per month 


State of Ohio, 
1894-1913 incl. 


o 
©^ 




©© 

°.o6 

00 


So 

0© 

°© 

OS 

105 
175 




-*^© 

O o> 

°o 

a-" 

46 
70 




= -• 
©_■ 

13 
24 



0© 

8 
11 




*OS 

©© 

2 
3 




©© 

°2 


1 


2a 
10" 



1 




■«© 
©© 
°© 

1 

1 




-^© 

0© 




°QO 

00 — ' 












424 

787 


188 
363 




372 sq. mi. per sta.. 
































Once in given number of years 




0.38|0.8l| 1.7| 4.2|l2 3|26.9| 99 1294 |294 1294 |. . . . 1. . . . 1 . . . . 1. . . .1 . . . . 




1 1 1 1 1 1 1 1 1 1 1 1 1 II 




Precipitation — inches per month 


State of Kansas, 
1894-1913 incl. 




©© 
©^ 


Q 

©© 

= 00 
00 




■"© 

©© 

°© 

© 




"a 

0© 

°o 

©•- 1 

58 
144 



*© 

©© 
©_^ 

45 

86 




~ 0. 
©© 
°.ci 

1M '"' 

20 

41 




■"as 
©© 
°co 

CO" - * 

8 




0© 

© ^ 

9 
13 




©© 
°. n 

1 

4 


O 

*© 

0© 

2 
3 


O 

«© 

o N 


1 


O© 

°oo 

00" 

1 
1 










Eastern section, 44 


231 
632 


146 
401 


111 
ass 




615 sq. mi. per sta., 


.... 






















Once in given number of years 




1.13 


1.8| 2.7| 5.0 


8.3 


17.4 


34.1 


55 


178 


2381 715| 715 




....1. ...!.... 






1 1 


Middle section, 35 


111 

264 


68 
H3 


35 

85 


23 
50 


12 

97 


6 
IS 


5 
9 


2 
4 




9 




9, 


2 












600 sq. mi. per sta., 


























Once in given number of years 




2.2 


3.8| 6.9 


ll.7|21.6 


39 


65 


146 


290| 290 


2901 






...I....I.... 








1 


Western section, 35 


44 
81 


10 

37 


10 

27 


11 
17 


3 
6 


3 
3 


















940 sq. mi. per sta., 
















i 
















Once in given number of years 


Frequency 


4.6 Il0.lll3.8l21.ol62.0l 124 i 


....|....|....|....|....|....|....|....|....|.... 














1 1 1 1 1 II 1 1 



128 



ELEMENTS OF HYDROLOGY 



TABLE 5. — RECORDS OF EXCESSIVE MONTHLY 
PRECIPITATION — (Concluded) 





Precipitation — inches per month 


State of Alabama, 
1894-1913 incl. 


2» 




oo 
®od 

00 

485 
1344 


5« 

O 

286 
859 


Q 

^0 
oo 

°o 

o — 

208 
573 


o 

-^o 

8" 

142 
365 


So 

oo 

93 
223 


So 

OCT> 

56 
130 


So 

°^ 

27 
74 


Q 

oo 

«,n 

22 

47 


So 

o» 

8 
25 


|o 

go 

9 
17 


o 
"o 

°™ 

2 

8 


So 

3 

6 


So 

o<=? 
=>o 

1 

3 


CO 

■*< 
CO 

CM 
1 

2 


CO 

CO 

to 

CM 






1 


812 sq. mi. per sta., 
Cumulative total 




1 




Once in given number of years 






0.59 0.92ll.38l2.16l3.55l 6.lll0.7ll6.8l31.6l 46 1 91 1 131 1 2631 394 


788 





































Typical Excessive Rainstorms. — A study has been made of 
typical storms of greatest recorded intensity in different parts 
of the United States. Maps of these storms are presented in 
Figs. 123 to 126 and the data on which the isohyetals are based 
are given in Tables 6 to 9. The relation between amount 
of precipitation and area covered by these severe storms is 
shown in Figs. 127 and 128. The Beaulieu, Minnesota, and the 
Fort Madison, Iowa, storms were also studied in connection 
with the resulting floods on the Wild Rice River and Devil's 
Creek, respectively; hence the watersheds of these streams 
are also shown on the maps. 

The storm paths are well indicated by the shape of the isohy- 
etals. The Iowa storm came from the West, the Minnesota 
storm from the Northwest, and the Arkansas and Illinois storms 
from the .Southwest. The first two storms lasted less than 
24 hours. The Arkansas storm was a part of the destructive 
West Indian hurricane of August, 1915, and lasted 2\ days. 
The Cairo, Illinois, storm extended over three days and was 
the greatest of all in extent and intensity. No serious floods 
resulted, however, because this storm centered over the lower 
reaches of large streams. The Ohio valley storm of March 23 
to 27, 1913, while of much less severity, resulted in unprece- 
dented stages on many streams because the heaviest precipi- 
tation occurred over the headwaters of the smaller northern 
tributaries. 



PRECIPITATION 



129 



Crookst 
0.00 a 




ne River Dam/ 



10 -.'0 SO 



Fergus Falla 
• 0.55 



Fort Ripley 



Fig. 123. — Map of Beaulieu, Minnesota, Storm, July 20, 1909. Less-than- 

one-day Storm. 



130 



ELEMENTS OF HYDROLOGY 




CO 



a 

O 

32 

e4 

5 



Ph 



PRECIPITATION 



131 




'32 



ELEMENTS OF HYDROLOGY 




3 4 5 6 

Area — Thousand Square Ifiles 

Fig. 127. 



14 

Q. 
CD 

Q 
8 10 

St 

u 

a 

M 

i 8 

I 6 



v 




































• 






















"*- 


-^^ 


~_^ 






2 


Hardy 
4 Days 

-AEgfl_< 


, Ark. Storm 
Aug. 18-20, 191, 
>f Entire Storm 


Ca 
3 


iro, Illi 
)ays-Oc 


aois Storm 
t. 4-6, 1910 












--Z 


^z: 


^- — 













~~JT- 
















- 


Porti 


2airo, Illinois £ 

Oct. 1-6, 19 

on Centering a 


torm — 
10 

Galcoi 


da 


"-? 


ortion L 


enterin 


g at Ha 


rdy 














1 1 
























RELATION 

OF 

DEPTH DP PRECIPITATION 




















AREA 


COVE 


TO 
RED E 


(Y ST< 


5RMS 









5 C 7 8 9 

Area - Thousand Square Miles 

Fig. 128. 



Waynesvlile 

lr S. 7.08* 




Perryville. 

6.76 



, Ironton 

4.80 



Jacka 
Marble Hill, y^- w 

6.05 





Fin. 12fi. — Map of Cairo, Illinois, Storm, October, I, r>, 6, 1010. Three-day Storm. 



PRECIPITATK )N 



133 



TABLE 6. — DATA FOR BEAULIEU, MINNESOTA, STORM 

July 20, 1909 

(Less than 24 hours) 





Precipitation — inches 




10th 


20th 


21st 


Plotted 


Angus Minn. 

*Crookston " 

Red Lake " 


3.11 
1.07 
2.70 
1.09 
f8.97 
1.20 
0.12 
0.97 
1.10 
1.40 
2.10 
0.16 

T 




T 
T 

0.12 
0.20 

10.00 
1.29 

10.75 
1.15 
1.00 
3.85 
4.17 
0.30 
1.07 
1.60 
0.55 
0.38 
0.05 


0.03 
0.16 

0.07 
0.16 
0.08 
0.72 
0.28 
0.38 
0.47 
1.25 
1.55 
4 50 
20 
1.20 
2.50 
1.38 
2.00 


12 


Kelliher " 


20 


Fosston " 

Bagley " 

*Halstad " 

Beaulieu " 


8.97 
10.00 

0.72 
10 75 


Cass Lake " 

Leech Lake, dam " 

State Sanatariura " 

! Park Rapids " 


1.15 
1.00 
3.85 
4.17 


Detroit. .' " 

Moorhead " 

Pine River dam -. . . . " 


0.30 
1.07 
1.60 


*Fort Ripley " 


0.55 
0.38 


Long Prairie " 


0.05 



* Precipitation for 24 hours ending on morning when measured. 
t Rain fell during night of 19th to 20th, 5.30 p.m. to 10.30 p.m. 



Precipitatioi 


Extent of storm area 
in square miles 


Over 1 in 


ch 10,590 


2 ' 


7,970 


" 3 ' 


5,750 


4 < 


4,180 


" 5 ' 


3,230 


U g , 


2,370 


" 7 ' 


1,660 


8 ' 


1,040 


9 ' 


566 


" 10 ' 


224 



Area of watershed of Wild Rice River at Twin Valley 805 square miles. Average precipitation 
over watershed 8.82 inches. 



134 



ELEMENTS OF HYDROLOGY 



TABLE 7. — DATA FOR FORT MADISON, IOWA, STORM 

June 9-10, 1905 

(Less-than-one-day storm) 



Station 



Chariton Iowa 

Corydon " 

Oskaloosa " 

Albia " 

Downing " 

Sigourney " 

Washington " 

Mt. Pleasant " 

Stockport " 

Keosauqua " 

Bonaparte " 

Gorin " 

Columbus, Jet " 

Wapello " 

Burlington " 

Ft. Madison " 

La Harpe " 

Keokuk " 

Warsaw " 

Colchester 111. 

Astoria " 

Peoria " 

Knoxville " 

Galva. " 

Cambridge " 

Aledo " 



Precipitation — inches 



9th 



4.22 

T 

1.30 



T 
0.09 



0.05 



0.10 
0.02 
0.06 



2.18 

0'05' 
0.04 
1.25 
0.15 
0.32 



10th 



3.56 
1.20 
3.44 
3.28 
2.73 
1.72 
7.20 
10.63 
11.09 
12.10 
1.83 
1.44 
2.00 
6.04 
6.40 
10.25 
2 62 
4.00 
4.70 
2.14 
2.54 
2.75 
2.98 
2.85 
78 



Plotted 



.22 
.56 
.50 
.44 
.28 
.82 
1.72 
7.25 
10 63 
11.09 
12.10 
1.83 
1.54 
2.02 
6 10 
6.40 
10.25 
4.80 
4.00 
4.75 
2.18 
3.79 
2.90 
3.30 
2.85 
0.78 





Extent of storm area in square miles 


Precipitation 














Center at Bonaparte 


Center at La Harpe 


Entire storm 


Over 4 inches 


4890 


2780 


7670 


" 5 " 


3575 


1865 


5440 


" 6 " 


2645 


1130 


3775 


" 7 " 


1837 


588 


2425 


" 8 " 


1172 


263 


1435 


9 " 


697 


70 


767 


" 10 " 


342 


10 


352 


" 11 " ....... 


123 
13 




123 


" 12 " 




13 









Area of watershed of Devil's Creek at railroad bridge 143.5 square miles. Average precipitation 
over watershed 8.72 inches. 



PRECIPITATION 



135 



TABLE 8. — DATA FOR HARDY, ARKANSAS, STORM 

August 18-20, 1915 

(Two-and-a-half-day storm) 



Station 



Springfield Mo. 

Hollister " 

*Mountain Grove " 

Houston " 

Gano " 

Birch tree " 

Goodland " 

*Ironton " 

Patton " 

Marble Hill " 

Jackson " 

Cape Girardeau " 

Sikeston " 

Poplar Bluff : " 

Doniphan " 

*New Madrid " 

Caruthersville " 

Cardwell " 

Koshkonong " 

Rogers Ark. 

Fayetteville " 

Eureka Springs " 

Dutton " 

Lutherville " 

Subiaco " 

*Dardanelle " 

Okay " 

Marshall " 

Bergman " 

Dodd City " 

*Calico Rock " 

Bee Branch " 

Conway ' 

*Georgetown " 

Seavey " 

*Newport " 

*Batesville " 

Alicia " 

*BlackRock " 

Hardy " 

Mammoth Springs " 

Pocahontas " 

Jonesboro " 

*MarkedTree " 

Wynne " 

tCairo 111. 



Precipitation — inches 



17th 18th 19th 20th 21st Plotted 



1.97 



T 
CK05 



1.45 
CK02 



0.22 

T 

T 



T 

1.68 



0.50 
0.05 
0.51 



1.35 



0.80 



0.08 



0.13 



0.17 
1.55 
2.04 
1.10 
2.16 
2.93 



0.52 
1.45 
1.25 
0.85 



1.26 
3.00 
4.00 
2.60 
1.65 
0.96 
2.87 
0.81 
1.49 
1.20 
1.73 
6.42 
1.87 



3.25 
2.45 



1.12 
0.25 



0.16 
0.45 
1.00 
4.08 
1.95 
5.45 
3.50 
3.50 
0.80 
0.01 



0.66 



3.04 
2.00 
0.68 
1.71 
1.14 
3.08 
2.85 
0.65 
0.95 
1.02 
4.10 



1.08 

0.86 

2.40 

2.40 

3.70 

2.82 
* 

4.09 
4.96 
5.43 
6.13 
0.25 
5.92 

2.00 

* 

6.33 

5.70 

* 

1.78 
4.90 
3.10 
2.19 



5.33 
2.05 
2.26 
2.50 
1.46 
6.70 
3.05 
3.80 
2.73 
1.80 
0.89 
1.34 



0.38 
1.40 
4.70 
2.30 
5.17 
2.28 
5.00 
6.70 
4.50 
4.61 
0.35 
3.35 



0.61 
0.41 
2.03 

0.28 



5.30 

10.90 

1.09 

1.43 

* 

6.10 
0.60 
0.11 
3.30 
0.87 
3.02 
5.44 
1.40 
2.11 
1.85 
3.94 



0.26 



1.40 



0.35 
0^13 



7.34 



9.30 
0.10 



0.04 



0.15 
T 



0.05 



0.10 



* Precipitation measured in morning. Amount then recorded is for preceding 24 hours. 

t Regular Weather Bureau Station precipitation is for 24 hours period, midnight to midnight. 



136 



ELEMENTS OF HYDROLOGY 



TABLE 8. — DATA FOR HARDY, ARKANSAS, STORM — (Concluded) 

August 18-20, 1915 

(Two-and-a-half-day storm) 





Precipitation 


Extent of storm area in square miles 




Center at 
Hardy 


Center at 
Marshall 


Entire storm 


0^ 


9 " 


12,600 

6,100 

2,380 

970 

460 

170 


6,400 
4,000 
1,010 


19,000 
10,100 




' 10 " 


3,390 
970 




' 11 " 




' 12 " 




460 




1 13 " 




170 











PRECIPITATION 



137 



TABLE 9. — DATA FOR CAIRO, ILLINOIS, STORM 

October 4, 5, 6, 1910 

(Three-day storm) 



Station 



Perry ville Mo. 

Jackson " 

Marble Hill " 

Doniphan " 

Sikeston " 

*New Madrid " 

Caruthersville ' 

Koshkonong ' 

Sparta III. 

Carbondale " 

Equality " 

*New Burnside " 

Cobden " 

Golconda " 

Cairo " 

*Chester. " 

Edwards ville " 

*E. St. Louis " 

Mascoutah. . . " 

Carlyle " 

Mt. Vernon " 

St. Peter " 

Flora " 

Olney " 

Sumner. " 

*Mt. Carmel " 

Albion " 

Fairfield " 

Corning Ark. 

Pocahontas " 

*BlackRock " 

Alicia. . " 

Jonesboro " 

*Batesville " 

*Newport " 

*MarkedTree " 

Earl _ " 

Mammoth Spring " 

Hardy " 

*Calico Rock " 

Bee Branch " 

Conway " 

DoddCity " 

Mossville " 

Lutherville " 

*Dardanelle. " 



3d 



3.52 
0.43 
T 
0.11 



0.11 
0.25 
0.76 



1.29 

0.28 

0.20 



0.81 



T 

0.19 
0.42 
T 



0.17 
1.23 
0.13 
1.32 
0.20 
0.70 
1.34 



0.06 



0.27 
T 



0.04 



Precipitation — inches 



4th 5th 6th 7th Plotted 



2.80 



2.40 
2.01 
5.50 
5.20 
4.15 
1.35 
2.18 
4.42 
5.24 
0.11 
5.10 
4.95 
4.47 
2.96 
0.42 
0.62 



1.40 
4.18 
1.55 
3.40 
2.69 
3.41 
3.10 
3.42 
3.85 
3.97 
2.23 



0.72 

9 



0.68 

1.14 

0.68 

0.50 

0.83 

t 

1.60 

1.03 

0.12 



2.00 
3.16 
3.20 
4.33 
4.00 
1.86 
3.10 
1.43 
1.15 
4.25 
5.47 
4.86 
4.60 
7.99 
4.77 
0.98 
3.05 
0.03 
2.87 
2.10 
0.45 



0.20 



35 
00 
8.50 
0.65 
2.79 
0.60 
3.52 
1.32 



0.95 

0.90 

1.05 

0.93 

1.90 

6.24 

3.00 

0.60 

0.51 

07 

01 

86 

10 

21 



0.42 
1.13 
0.50 
2.33 
0.45 
0.60 
1.64 
0.35 
0.85 
0.52 
0.87 
2.76 
1.23 
1.31 
1.40 
1.35 



1.00 



6.00 
7.45 
0.84 
0.90 
0.65 
1.00 
2.50 
0.86 



0.52 
3.44 



0.11 



1.37 



0.02 



5.75 

7.58 

6.65 

7.27 

11.40 

13.30 

10.25 

3.38 

3.84 

9.74 

12.75 

12.09 

10.80 

15.18 

9.66 

5.07 

3.97 

2.98 

3.32 

4.10 

6.27 

3.65 

6.75 

5.61 

7.33 

7.92 

6.87 



95 
37 

72 
31 
20 
6.50 
5.70 
9.20 
13.99 
4.97 
3.46 
5.14 
3.68 
11.50 
2.34 
2.79 
2.20 
5.07 
4.88 



* Precipitation for the 24 hours ending on the morning when it is measured, 
t Precipitation included in that of the next measurement. 



138 



ELEMENTS OF HYDROLOGY 



TABLE 9. — DATA FOR CAIRO, ILLINOIS, STORM 
October 4, 5, 6, 1910 

(Three-day storm) 



(Continued) 





Precipitation — inches 




Station 












3d 


4th 


5th 


6th 


7th 


Plotted 


*Wynne Ark. 




2.02 


1.89 


4.60 


0.01 


8.51 


Brinkley " 




0.78 


0.52 


2.61 




3.91 


*Owensboro Ky. 




0.20 


2.62 


5.31 


0.33 


8.26 


Calhoun. " 


T 


1.37 


3.88 


4.82 




10.07 


*Beaver Dam " 








4.30 
5.60 


0.50 
0.15 


4.80 


*Earlington " 


0.07 




1.06 


6.81 


*Hopkinsville " 




1.00 


1.20 


3.85 




6.05 


Cadiz " 


0.17 


0.97 


7.08 


0.74 




8.79 


Marion " 


T 


1.75 


4.92 


•2.78 




9.45 


*Paducah " 




1.90 


2.00 


5.00 


0.12 


9.02 


Blandville " 


0.30 


4.23 


4.29 


1.78 




10.30 


Lynville " 


T 


1.32 




5.50 




6.82 


Kenton Tenn. 


0.47 


1.36 


1.50 


4.90 




7.76 


*Dyersburg " 




0.67 


1.00 


6.20 




7.87 


*Covington " 




0.75 


0.08 


8.35 


0.10 


9.18 


Memphis " 


0.55 


0.01 


3.65 


0.52 




4.18 


Jackson -. " 




0.50 


3.10 


0.05 




3.65 


*Arlington " 




0.78 


T 


3.20 


T 


3.98 


*Brownsville " 




0.25 
0.01 


0.19 
0.41 


6.00 
5.25 


0.98 
0.10 


7.42 


*Milan " 


5.67 




T 


0.30 


2.00 


4.00 




6.30 


Union City " 




1.87 


2.25 


2.27 


0.12 


6.39 


Dover " 




0.60 


1.60 


4.07 




6.27 


Springville " 




0.22 


1.19 


4.54 




5.95 


Mt. Vernon Ind. 




2.36 


3.32 


4.36 


0.10 


10.04 


Evansville " 


0.17 


3.66 


6.50 


0.55 




10.71 


Rome " 




0.95 


2.60 


4.48 


0.01 


8.03 


Princeton " 




2.83 
3.70 


3.50 

4.45 






6.30 


Huntingburg. . " 


2.15 




10.30 


Paoli " 




1.95 


4.37 


1.80 




8.12 


Vincennes " 




2.80 


2.00 


3.20 


T 


8.00 


Farmersburg " 


0.05 


2.10 


1.99 


0.57 




4.66 


Worthington " 




1.71 


3.90 


0.75 




6.36 


Marengo " 




0.41 


4.00 


0.89 




5.30 


Salem " 




1.10 


4.80 


2.57 




8.47 






0.75 


2.25 


3.37 




6.37 


Scottsburg " 




0.36 


4.96 


2.90 




8.22 


Seymour " 




0.92 


3.70 


1.88 




6.50 


Bloomington " 




0.70 


4.00 


4.02 


0.08 


8.72 


Columbus " 




0.14 


4.12 


4.00 


0.24 


8.26 


Shelbyville " 




1.77 


3.05 


1.53 




6.35 


Greensburg " 




0.87 


4.02 


1.82 




6.11 


Butlerville " 




0.30 


4.88 


3.38 




8.56 


Madison " 




0.54 


2.43 


4.86 




7.83 


Moore's Hill " 




0.09 
1.27 


4.03 
3.99 


4.30 
1.65 




8.42 


Mauzy " 


6.91 


Connersville " 




0.88 


4.29 


1.85 




7.02 


Cincinnati Ohio 




0.26 


2.33 


2.82 




5.41 


Jacksonburg " 




0.11 




7.50 




7.61 






0.06 


3.82 


2.78 




6.66 


Waynesville " 






3.30 


4.38 




7.68 









Precipitation for the 24 hours ending on the morning when it is measured. 



PRECIPITATION 



139 



TABLE 9. — DATA FOR CAIRO, ILLINOIS, STORM 
October 4, 5, 6, 1910 
(Three-day storm) 



(Concluded) 





Extent of storm area in square miles 


Precipitation 


Center at 

Bee Branch, 

Ark. 


Center at 

Marked 

Tree, Ark. 


Center at 

New 

Madrid, Mo. 


Center at 

Galconda, 

111. 


Center at 
Hunting- 
burg, Ind. 


Entire 
storm 


Over 7 inches 
" 8 " 
9 " 
" 10 " 
" 11 " 
« 12 << 


3190 

1850 

972 

356 

44 


5860 

4110 

2560 

1500 

780 

375 

92 


7440 
5400 
3820 

2285 

1070 

360 

28 


10,980 

8720 

6490 

4490 

2530 

1365 

655 

217 

18 


14,330 

7780 

2210 

805 


41,800 

27,860 

16,052 

9,436 

4,424 

2,100 

775 


" 13 " 




ii 14 << 




217 


ii 15 a 






18 











Area Covered by Excessive Storms. — Friihling concluded 
from observations at Breslau, Germany, that the rate of pre- 
cipitation 10,000 feet from the center of a storm was one half 
the maximum and that the reduction in intensity was along a 
parabolic curve. He deduced the formula (reduced to feet) : 

R = 1 - 0.0028 VL 



where R represents the ratio between intensity of precipitation 
at L feet from the center to that at the center. According to 
this formula, excessive rain storms cover an area about 15 miles 
in diameter. 



140 



ELEMENTS OF HYDROLOGY 



Estimating Probable Maximum Precipitation on Watersheds. 

— By superimposing storm maps upon maps of the watersheds 
of different streams in the region in which the storms occurred, 
giving due consideration to storm paths, a good estimate can 
be made of the probable maximum amount of precipitation 
which may be expected on the watershed in the given time. 



'> - — — - . 




Fig. 129. — Map of Stanley, Wisconsin, Storm, October 6, 1911. Average 
Precipitation over Black River Watershed above Black River Falls, 3.00 ins. 

For example, the Stanley, Wisconsin, storm of October 6, 1911, 
Fig. 129, when moved a little further to the east, Fig. 130, re- 
sults in an increase in the 24-hour average precipitation on the 
watershed above Black River Falls from 3.00 to 3.69 inches. 
The Beaulieu, Minnesota, storm of July, 1909, would have 
caused an average precipitation of 6.1 inches over the water- 
shed of the Black River above Black River Falls and 7.2 inches 



PRECIPITATION 



141 



over the watershed above Neillsville. The Merrill, Wisconsin, 
storm of July, 1912, would have resulted in an average pre- 
cipitation over these watersheds of 4.8 inches and 6.4 inches, 
respectively. This Merrill storm, averaging 4.1 inches over the 
watershed of the Wisconsin River above Wausau caused a flood 
at Wausau which was 1.8 feet higher than the highest previous 



# Downing 




• Reeds Landing: 



SCALE OF MILES 



Fig. 130. — Stanley, Wisconsin, Storm of October 6, 1911, transposed. 
Average Precipitation over Black River Watershed above Black River 
Falls, 3.69 ins. 

record, that of September, 1881. It is interesting to note, 
however, that notwithstanding this fact the Beaulieu, Minne- 
sota storm of July, 1909, would have caused a still greater pre- 
cipitation, viz., 6.4 inches, over this watershed. 

From a study of Wisconsin and Illinois rainfall, Stewart * 
* Stewart, C. B., West. Soc. Engrs., 1913, p. 290. 



142 



ELEMENTS OF HYDROLOGY 



concluded that once in about 50 years the following amounts 
of precipitation might be expected in the given time and over 
areas of from 500 to 2500 square miles. 

PROBABLE MAXIMUM RAINFALL OCCURRING 
ABOUT ONCE IN FIFTY YEARS 





Inches rainfall over 


Days 












500 sq. mi. 


1000 sq. mi. 


2500 sq. mi. 


2 


10 


8 


6 


4 


11 


9 


7 


10 


13 


HI 


10 


30 


15 


14 


13 



Fig. 131 gives the precipitation in 2, 3 and 4 days in the state 

of Ohio during the storm of March, 1913. The data for the 

2- and 4-day storms of this Figure are based upon Bulletin Z 

12 r 



10 



O 8 



"S 4 




DEPTH OF PRECIPITATION 

TO 
AREA COVERED BY STORM 



12 16 20 24 28 

Area Thousand Square Miles 

Fig. 131. 



32 



36 



40 



of the U. S. Weather Bureau; that for the 3-day storm is based 

upon Prof. Sherman's paper, "■ The Ohio Water Problem." 

Morgan * gives the following rates of rainfall for the greatest 

recorded 1-, 2- and 3-day storms in the upper Mississippi valley. 

* Morgan, Arthur E., Report to the Board of Directors of the Miami Con- 
servancy District. 



PRECIPITATION 



143 



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144 ELEMENTS OF HYDROLOGY 

Hourly Rates of Excessive Precipitation. — In municipal 
improvement work, particularly in the design of sewerage 
and drainage systems, and works for the collection of water 
running off from small watersheds, the amount of precipitation 
which may be expected in one or two hours, and in less than 
hourly periods of time, is of great importance. The frequency 
with which given rates of precipitation may be expected to 
recur should be the basis of design, but whether an installation 
which is designed to care for all rates of precipitation that may 
be expected once in 1 year, or once in 10 or 100 years, or in 
any intermediate time interval, will best serve a given com- 
munity, the engineer must determine in each individual in- 
stance. In the following pages, the author has summarized most 
of the available data relating to excessive precipitation in the 
United States east of the Rocky Mountains, and has presented 
a number of new formulas giving the amount and rates of pre- 
cipitation from 5 to 120 minutes time which, on an average, 
will probably be exceeded once in intervals of from 1 to 100 
years. 

Most studies of rates of excessive precipitation, made here- 
tofore, have been based upon an analysis of the records of single 
observation stations. In view of the irregular manner in which 
precipitation occurs, with respect to time, in any given locality, 
however, the records of a single station furnish a far less satis- 
factory basis for a conclusion regarding the frequency of given 
rates of excessive precipitation than the records of several 
stations in the same locality. 

Intense rainstorms usually cover only a few square miles. 
Observation stations five or ten miles apart usually show about 
as much dissimilarity in the rates of excessive precipitation 
during intense rainstorms as stations 50 or 100 miles apart. 
As there are only about 200 Weather Bureau stations in the 
United States at which continuous records of precipitation 
are being secured, it is apparent that only a very few of the 
excessive rainstorms which actually occur, arc being recorded. 



PRECIPITATION 145 

In a few of the larger cities, of course, municipal organizations 
are maintaining a number of observation stations and are thus 
obtaining more complete data. 

The records of adjacent observation stations well indicate 
the irregular manner in which excessive precipitation occurs. 
During the New York City storm of October 1, 1913, for example, 
(Fig. 132) twice as much rain fell in two hours at Borough 
Hall in the Borough of Richmond, than at the United States 
Weather Bureau station in the Borough of Manhattan, five 
miles away. It is safe to say that, taking the country as a 
whole, doubling the number of Weather Bureau observation 
stations would double the number of records of excessive pre- 
cipitation obtained. For the same reason, the records of several 
stations in one region are virtually equivalent to a longer record 
at a single station. One record supplements the other, making 
a combined record which is far more representative of the rates 
of precipitation to be expected in the given region than the 
records of a single station. 

Table 11 is a summary of the number of intense rainstorms 
during which given rates of precipitation have been exceeded 
at 43 United States Weather Bureau stations during the 19 
years between 1896 and 1914. The extent to which the records 
of one station supplement those of another in the same part of 
the country is apparent from a study of this table. Stations 
with a disproportionate number of very excessive storms have 
usually had a deficiency of ordinary storms. Other stations 
that have experienced many short storms have had comparatively 
few long ones and vice versa. 

In studying the observational data, the entire 1962 storms 
were first analyzed, and the greatest amount of precipitation 
which occurred at any time during the storm within a continu- 
ous period of 5, 10, 15, 30, 60, 100 and 120 minutes time was first 
determined. If a storm lasted only 60 minutes, the observed 
precipitation in that length of time was considered as also hav- 
ing fallen within 100 and 120 minutes time. While this is 



146 ELEMENTS OF HYDROLOGY 

virtually equivalent to assuming the precipitation which oc- 
curred in a given period of time as having been uniformly 
distributed over that time, nevertheless, it is believed that 
the estimates of the lengths of time required for the runoff 
from a given precipitation to reach various points of concen- 
tration in a sewer system, for example, are usually far more 
in error than the assumption of uniform, or progressively de- 
creasing, rates of precipitation over periods of 15, 30, 60, or even 
120 minutes of time. In other words, the author believes that 
the amount of precipitation which falls in a given period of 
time, even though not uniformly distributed over that time, 
nevertheless furnishes information which is fully as accurate as 
the other information and assumptions which enter into the 
computations of runoff into sewerage and drainage systems. 
The restriction of precipitation studies to storms of uniform 
rates does not appear warranted. 

Table 12 gives the observational data for 100 typical intense 
storms in the United States east of the Rocky Mountains 
and Figs. 132 to 138 show graphically the precipitation during 
a few of the most exceptional storms, both in proper sequence 
of time as it actually occurred, and also when arranged in the 
order of maximum accumulated amounts of precipitation in 
the given time intervals. 

Table 13 is a summary of these storms giving only the most 
exceptional rate of precipitation, together with similar records 
of the most exceptional earlier rainstorms. 

From the records of the individual observation stations, the 
rate of precipitation which would probably be exceeded with 
frequencies of once in 1, 2, 5 and 10 years were first selected. 
Stations showing similar rates were placed in one group. These 
data appear in Table 14. From the combined records of all the 
stations in each group the rates of precipitation which would 
probably be exceeded in 1, 2, 5, 10, 25, 50 and 100 years were 
then determined and formulas worked up which best fitted the 
observational data. It was found that the precipitation varied 



PRECIPITATION 



147 



6.0 



h4.0 



i 

p.3.0 



3.0 



1.0 









































^^ 


„^= 


^. 






NEW YORK CITY, STORM 
October 1, 1913 




S* y^ 












Ma 


ximum 1 
iu giv 


'recipita 
n Time 

/ 


tion,o • 


/ 


f Actual Observed. 
_/ Precipitation 




^^. 








/ 
/ 
/ 


Depa 
Public 

' Boroii] 
Richm 


•tment c 
Works,/ 
fhofZ 
and/ 


t^r Maximum Precip 
in give'u Time,- 

. — rxCJ 


tatiou, ^ 










> 
/ 

// 


/ 


-"'' y 


'/ U.S. Weath 

Station Bo 

of Manha 


2r Burea 
ough y 
ttan / 


u/ 












/ ,' 






^-Actual Observed. 
Precipitation 













50 60 70 

Time - Minutes 

Fig. 132. 



100 



110 120 




10 20 

Time - Minutes 

Fig. 133. 




10 20 30 

Time - Minutes 

Fig. 134. 



5.0 



1.0 



5 3.0 



!3.0 



1.0 



















































/Ci 


ctual Oi 


served 


















Precipitation 








Maximum 


^r 










Precipitation y 








MADISON, WIS., STORM 




{ in Given ^/ 












\. Time /S 








AUG. 8, 1906 






s / 












/ 




















/ , 








































/ / 




















/ / 




















// 





















10 



20 



40 50 00 

Time -Minutes 

Fig. 135. 



70 



90 



100 



«.o 



5.0 



24.0 



!3.0 



'2.0 



1.0 































































Maximum Pre 
in given r 


cipitatioii /'j 
'irae I ""?/ / 


















Y /■■ 


















A / 












/ y 




KANSAS CITY, MO. STORM 










Actual O 


iserved 


August 23, 1906 




j 


/ 
/ 
/ A 

/ / 


















/ 

/ 

/ . 

/ / 





















10 30 30 40 50 60 70 80 90 100 

Time - Minutes > 



Fig. 136. 



5.0 



4.0 



<:u) 



: 2.0 



l.o 



































^Actu 


al Obsei 


ved 
















P 


•ecipitat 


on 




Ma' 
Prec 
inGi 

Tim 


rmum 
lpitation 


s/ 




DODGE CITY, KAN., STORM 

SEPTEMBER 16, 1906 




/ J 
// 
// 





















10 20 30 40 50 60 70 80 90 100 

Time -Minutes 

Fig. 137. 









ll.'r 


7 i 
// 


4 


/ 










































w 






S 


< % 




























S- 


^, 














.»v 


«£■ 


^-1 


















^ 


90^. 


S- 


io^£ 


95 






























0« 


^22 












: 


.(at 


i D 


iag 


■an 


























































/ 




























































































































# 


& 
















TYPICAL GALVESTON STORMS 












^ 


y/ 

























































































































0:15 0:3« 0;1S 1:00 1:30 2:00 2:30 3:00 3:30 4:00 4;30 5:00 5:30 6:00 
Time— Hours and Minutes. 
(148) Fig. 138. 



PRECIPITATION 149 

At 
most nearly as the formula Q = . „ where Q is the precipi- 
tation in inches, t the time in minutes, and A and B are 
constants. The frequency of different rates of precipitation 
varies approximately as F°' 2 where F represents the number 
of years between recurrences of rates of precipitation exceed- 
ing the given intensity. The exponent of F is less than .2 
for 5- and 10-minute rates and greater for 100- and 120-minute 
rates, varying from about .15 to .3. 

The author's formulas for the five groups of stations in the 
United States east of the Rocky Mountains, together with the pre- 
cipitation to be expected in given time intervals of less than two 
hours, with frequencies of from once a year to once in 100 years, 
are given in Table 15. It is believed that the rates of precipi- 
tation here given furnish a better basis for design than those 
determined from the records of individual stations. Considering 
a long period of years, the amounts and rates of precipitation 
given, by the formulas of this table will all be exceeded with 
equal frequency. 

As the records of no stations used in this study of excessive 
precipitation extend over more than 19 years, it would obvi- 
ously be impossible to determine, from the records of one station, 
the probable intensity of rates of precipitation which occurred 
with less frequency than once in 5 or 10 years. The combined 
records, however, indicate that some of the storms which have 
occurred within the last 20 years are not likely to recur at 
the same station with a greater frequency than once in 100 or 
more years. 

For example, at Galveston, Texas, three storms have occurred 
in recent years which had an intensity which is to be expected 
only about once in 100 years. In all three of these storms 
the precipitation amounted to over 6 inches in two hours. The 
exceptional character of these storms is well indicated by the 
fact that no other storms occurred in the 19 years from 1896 to 
1914 in which more than 4 inches of rain fell in two hours 



150 ELEMENTS OF HYDROLOGY 

The storm of August 8, 1906, at Madison, Wisconsin, was 
still more exceptional in character for this region. Over 4^ inches 
of rain fell in two hours, yet, not another rainstorm occurred 
at this station during the period from 1905 to 1914 in which 
the precipitation exceeded \\ inches in two hours. It is prob- 
able that the storm of August 8, 190G, will not be equaled at 
this station in several hundred years. 

Other storms in which rain fell at rates that will probably 
not be equaled, at the given stations, in several hundred years 
are the storms of August 23, 1906, at Kansas City, Mo., of Oc- 
tober 13, 1913, at New York City, Borough of Richmond, of 
June 18, 1911, at Augusta, Ga., and of April 29, 1905, at Taylor, 
Texas. 

Table 16 gives the principal formulas proposed in the past for 
the determination of rates of excessive precipitation in different 
sections of the United States. By reference to Table 15 the 
precipitation given by these formulas can be compared with 
that given by the author's formulas. 

Index Map. — Fig. 139 shows the location of Weather Bureau 
observation stations used in the rainfall studies just discussed 
and the boundaries of the areas to which the several formulas 
for frequency of excessive rates of precipitation apply. 



PRECIPITATION 



151 




152 



ELEMENTS OF HYDROLOGY 



TABLE 11. — SUMMARY OF RECORDS OF INTENSE RAIN- 
STORMS AT FORTY-THREE STATIONS — 1896-1914 
Group No. 1 (57 Station-years) 



Precipitation in 5 minutes 


No. of storms of given intensity at 


Total No. of 
storms exceed- 


Galveston 


New 

Orleans 


Jacksonville 


Total 


ing given 
intensity 


0.40-0.44 
0.45-0.49 
0.50-0.54 
0.55-0.59 
0.60-0.69 
0.70-0.79 


5 
5 
8 
2 
3 


12 
4 
5 
5 

1 


11 

7 
9 
3 
3 
1 


28 
16 
22 
10 
7 
1 


84 
56 
40 

18 
8 
1 



In 10 minutes 












0.60-0.69 


20 


23 


20 


63 


140 


0.70-0.79 


9 


12 


10 


31 


77 


0.80-0.89 


4 


5 


10 


19 


46 


0.90-0.99 


8 


3 


6 


17 


27 


1.00-1.09 


2 


2 


1 


5 


10 


1.10-1 19 


1 


3 


1 





5 



In 15 minutes 












0.80-0.89 


12 


18 


11 


41 


130 


0.90-0.99 


15 


13 


8 


36 


89 


1.00-1.09 


2 


8 


9 


19 


53 


1.10-1.19 


3 


2 


5 


10 


34 


1.20-1.39 


7 


4 


3 


14 


24 


1.40-1.59 


3 


2 


4 


9 


10 


1.60-1.79 




1 




1 


1 



In 30 minutes 












1.30-1.39 


4 


10 


6 


20 


76 


1.40-1.49 


3 


5 


2 


10 


56 


1.50-1.59 


4 


5 


4 


13 


46 


1.60-1.69 


2 


5 


1 


8 


33 


1.70-1.79 


3 


2 





5 


25 


1.80-1.99 


3 


4 


1 


8 


20 


2.00-2.19 


1 


1 


3 


5 


12 


2.20-2.39 


2 


1 


1 


4 


7 


2.40-2.59 












3 


2.60-2.79 


2 






2 


3 


2.80-2.99 


1 






1 


1 



In 60 minuteo 












1.70-1.79 




2 





2 


60 


1.80-1.99 


8 


7 


6 


21 


58 


2.00-2.19 


5 


4 


3 


12 


37 


2.20-2.39 


6 


1 


3 


10 


25 


2.40-2.59 


2 


4 





6 


15 


2.60-2.79 





1 





1 


9 


2.80-2.99 





1 


1 


2 


8 



PRECIPITATION 



153 



TABLE 11. — SUMMARY OF RECORDS OF INTENSE RAIN- 
STORMS AT FORTY-THREE STATIONS — 1896-1914 — (Continued) 
Group 1 (57 Station-years) 



Precipitation 


No. of storms of given intensity at 


Total No. of 
storms exceed- 


in 60 minutes 


Galveston 


New 
Orleans 


Jacksonville 


Total 


ing given 
intensity 


3.00-3.24 
3.20-3.39 
3.40-3.59 
3.60-3.79 
3.80-3.99 
4.00-4.49 
4.50-4.99 
5.00-5.49 


1 
1 



2 

1 




1 


2 
1 





2 

1 


6 
4 
3 
3 
3 
3 
1 
1 



In 100 minutes 












1.80-1.99 


6 


10 


5 


21 


76 


2.00-2.19 


6 


5 


3 


14 


55 


2.20-2.39 


3 


3 


6 


12 


41 


2.40-2.59 


2 


4 





6 


29 


2.60-2.79 


4 





2 


6 


23 


2.80-2.99 


1 


1 


1 


3 


17 


3.00-3.24 


2 


1 


2 


5 


14 


3.25-3.49 


2 


2 




4 


9 


3.50-3.74 


1 







1 


5 


3.75-3.99 





1 




1 


4 


4.00-4.49 












3 


4.50-4.99 












3 


5.00-5.49 












3 


5.50-5.99 


1 






1 


3 


6.00-6.49 












2 


6.50-6.99 


2 






2 


2 



In 120 minutes 












1.90-1.99 


2 


3 


1 


6 


63 


2.00-2.19 


6 


4 


4 


14 


57 


2.20-2.39 


4 


4 


5 


13 


43 


2.40-2.59 


2 


4 


1 


7 


30 


2.60-2.79 


4 








4 


23 


2.80-2.99 


1 


1 


2 


4 


19 


3.00-3.24 


1 


1 


2 


4 


15 


3.25-3 49 


1 


1 





2 


11 


3.50-3.74 


2 








2 


9 


3.75-3.99 


1 


1 


1 


3 


7 


4.00-4.49 





1 




1 


4 


4.50-4.99 












3 


5.00-5.49 












3 


5.50-5.99 












3 


6.00-6.49 


1 






1 


3 


6.50-6.99 


1 






1 


2 


7.00-7.99 


1 






1 


1 



154 



ELEMENTS OF HYDROLOGY 



TABLE 11. — SUMMARY OF RECORDS OF INTENSE RAIN- 
STORMS AT FORTY-THREE STATIONS— 1896-1914 — (Cont'd) 
Group No. 2 (260 Station-years) 













No. of storms of given intensity at 








Total 






























No. of 
storms 
exceed- 
ing 
given 
inten- 
sity 


Precipita- 
tion in 5 
minutes 


u 
O 


.2 
2 
a. 
"3 

T3 

J5 

PL, 


a 
o 

2 

03 


3 
o 


- 

"3 


.13 
03 
O 

c 

03 

> 
03 

02 


03 

a 
< 


o 
o 

3 


J3 
O 




01 

a 

2 


OJ 

c 
o 

« 


3 
O 
Hi 


>> 

o 

03 

a 

03 

W 


a 

o 

a 
3 


o 

c 

'o 

§ 

o 

Q 


"c3 
O 

E-i 


0.35-0.39 


6 


8 


13 


12 


11 


21 


7 


6 


7 


6 


6 


5 


9 


7 


7 


131 


282 


0.40-0.44 


3 


2 


6 


5 


7 


4 


2 


5 


7 


2 


3 


5 


2 


8 


3 


64 


151 


0.45-0.49 





3 


3 


6 


4 


1 


2 


2 


3 


3 








2 


2 


5 


36 


87 


0.50-0.54 


2 


2 


3 





1 


1 


2 


1 





1 


1 





3 





2 


19 


51 


0.55-0.59 








1 


2 


3 


1 


2 




1 




1 





2 








13 


32 


0.60-0.69 


1 


2 


1 


1 





?, 


1 








1 


2 


1 


2 


1 


15 


19 


0.70-0.79 










1 














1 
1 



1 






2 
2 


4 


0.80-0.89 






















2 





























In 10 min. 




































0.50-0.54 


3 


4 


8 


10 


15 


16 


10 


11 


13 


2 


7 


8 


15 


9 


3 


134 


515 


0.55-0.59 


4 


9 


8 


13 


10 


17 


6 


8 


5 


6 


2 


2 


11 


4 


10 


115 


381 


0.60-0.69 


5 


7 


17 


16 


13 


17 


13 


4 


14 


7 


8 


5 


8 


9 


8 


151 


266 


0.70-0.79 


2 


3 


4 


5 


5 


1 


2 


6 


6 


3 


1 


5 


3 


5 


4 


55 


115 


0.80-0.89 


1 


2 


3 


3 


4 





1 


1 


2 


1 


1 


2 


2 


2 


3 


28 


60 


0.90-0.99 


1 


3 


1 


2 


?, 


3 


1 











2 


1 





1 


17 


32 


1 00-1 09 




1 




1 

1 




1 

1 


1 


1 









1 




3 
1 



1 
1 



1 


7 
4 
4 


15 


1 10-1 19 








8 


1 20-1 39 












4 























In 15 min. 

0.65-0.69 
0.70-0.79 
0.80-0.89 
0.90-0.99 
1.00-1.09 
1 . 10-1 . 19 
1.20-1.39 
1.40-1.59 
1.60-1.79 



7 


2 


9 


8 


6 


17 


4 


13 


8 


6 


3 


5 


8 


4 


10 


110 


3 


8 


10 


16 


12 


20 


10 


11 


11 


7 


7 


5 


15 


13 


8 


156 


3 


8 


13 


11 


12 


7 


11 


6 


8 


4 


2 


3 


5 


4 


3 


100 


2 


3 


3 


3 


4 


5 


4 


1 


6 





3 


6 


5 


6 


5 


56 


1 


1 


1 


4 


3 





2 


3 


2 


1 





3 


1 


1 


1 


24 








1 


2 


3 


2 







3 


2 








2 


1 


2 


18 


1 


1 


3 


2 
2 


1 


2 


1 


2 


2 









1 







2 
1 



1 
1 


2 


15 
6 
4 







































In 30 min. 

0.90-0.99 

1.00-1.09 

1 . 10-1 . 19 

1.20-1.39 

1.40-1.59 

1.60-1.79 

1.80-1.99 

2.00-2.19 

.20-2.39 

.40-2.59 

.60-2.79 

.80-2.99 

.00-3.24 



7 


8 


11 


14 


7 


14 


7 


6 


11 


7 


9 


5 


9 


8 


4 


127 


2 


6 


3 


6 


12 


9 


5 


9 


5 


3 


6 


5 


9 


7 


7 


94 


4 


3 


3 


5 


10 


6 


3 


5 


5 


2 


2 


4 


7 


5 


2 


66 


1 


1 


6 


6 


2 


9 


7 


3 


12 


3 


1 


3 


4 


6 


6 


70 


2 


3 


7 


5 


7 


6 


3 


3 








2 


2 


7 


1 


2 


50 





2 


2 


2 


2 


3 


3 


2 


2 





1 


1 


1 


1 


3 


25 





1 


1 









1 


1 


1 


2 






1 


1 




9 


1 



1 


1 




2 

1 




1 




1 


1 







1 




1 




2 




7 
2 
3 


1 















































































































TABLE 11. — SUMMARY OF RECORDS OF INTENSE RAIN- 
STORMS AT FORTY-THREE STATIONS — 1898-1914 — (Cont'd) 
Group No. 2 (260 Station-years) 



No. of storms of given intensity at 



Total 
No. of 
storms 
exceed- 
ing 
given 
inten- 
sity 



340 

266 

212 

169 

141 

95 

35 

42 

23 

18 

11 

7 

3 

2 

1 

1 

1 



1 


1 


4 


4 


6 


5 


4 


2 


8 


1 


3 


9 


4 


5 


2 


59 





2 


2 


5 


10 


6 


3 


5 





2 


1 


4 


1 


1 


1 


43 


2 


2 


2 


2 


3 


4 


3 


2 


5 


1 


2 


3 


2 


2 


1 


36 


7 


2 


6 


4 


2 


5 


2 


5 


4 


2 


1 


3 


9 


3 


1 


56 





1 


3 


4 


3 


6 


6 


1 


3 


1 


2 


1 


6 


3 


1 


41 


3 


2 


1 





1 


1 





2 


1 











2 


2 


2 


17 





2 





1 


2 


2 


4 


2 


4 





1 





2 


1 





21 


1 





3 





2 


4 





3 








1 








1 





15 





1 

















1 













2 


3 


1 


8 








1 





1 


1 







1 







1 


1 


1 





7 


1 






2 


1 








1 










1 




1 






2 


2 
1 


10 
2 




























1 






1 






2 




1 





1 







1 




1 




1 











1 






2 
3 


1 

























































323 

264 

221 

185 

129 

88 

71 

50 

35 

27 

20 

10 

8 

6 

4 

1 

1 

1 



In 120 min. 




































1.40-1.49 





2 


3 


5 


9 


6 


3 


3 





1 


1 


3 


1 


1 


1 


39 


265 


1.50-1.59 


1 


2 


2 


1 


3 


4 


3 


3 


4 


2 


2 


4 


1 


2 


1 


35 


226 


1.60-1.79 


5 


2 


6 


5 


3 


5 


2 


5 


5 


2 


1 


2 


8 


3 


1 


55 


191 


1.80-1.99 


2 





2 


4 


3 


5 


5 


2 


3 


1 


2 


3 


8 


3 


1 


44 


136 


2.00-2.19 


3 


1 


1 





1 


2 





2 


1 











2 


2 


2 


17 


92 


2.20-2.39 


1 


2 


1 


1 


2 


2 


5 


2 


3 





1 





2 


1 





23 


75 


2.40-2.59 





1 


3 





2 


3 





2 


1 




















12 


52 


2.60-2.79 


1 


1 











1 























1 


1 


5 


40 


2.80-2.99 








1 





1 











1 








1 


1 


3 





8 


35 


3.00-3.24 








1 







1 


1 


2 











1 





2 


1 


9 


27 


3.25-3.49 


1 





1 


1 

















1 




1 


1 


2 


8 


18 


3.50-3.74 
























1 






2 






3 


10 


3.75-3.99 
























1 













1 


7 


4.00-4.49 




1 






1 






1 




1 


1 









1 






4 
1 

1 


6 


4.50-4.99 






2 


5.00-5.49 
























1 


5.50-5.99 


























1 































(155) 



156 



ELEMENTS OF HYDROLOGY 



TABLE 11.— SUMMARY OF RECORDS OF INTENSE RAIN- 
STORMS AT FORTY-THREE STATIONS. — 1896-1914 — (Cont'd) 
Group No. 3 (317 Station-years) 















No. of storms of 


given i 


q tensity at 












Total 
No. of 


Precipita- 
tion in 5 
minutes 


a 
5 

o 

n 


>> 
a 

s 

< 


M 

3 

s 


en 

a 

s 


< 


c 
c 

M 


1= 
5 


g 

O 



a 

03 


■3 

B 


O 


'3 

a 

O 


13 

a 

> 




I 


C 


•0 a 
c g 

2 - 
OK 




M 

03 



O 


c 



-a 

n 


3 
OS 

02 


0) 

8 


a 



-2 
a 




ar 

C 

c 


"3 

H 


storms 
exceed- 
ing 
given 
inten- 
sity 


0.35-0.39 
0.40-0.44 
0.45-0.49 
0.50-0.54 
0.55-0.59 
0.60-0.69 


2 
1 



1 


5 
3 
2 

2 


2 
4 

1 
1 


5 
4 
1 
1 
1 


8 
2 
3 

1 

1 


8 
1 
3 


5 
1 
1 



1 


4 
1' 
1 
1 


10 
4 
1 
3 

1 


2 
1 
2 
1 


3 
1 

2 

1 
1 


7 
4 
3 
1 


1 
2 


7 
1 
1 
1 
2 


4 




1 


4 
3 
6 
1 
1 


1 




1 


4 
2 
1 
2 


3 
3 
4 
2 
1. 


85 
38 
29 
16 
11 
3 
3 


185 
100 
62 
33 
17 
6 


0.70-0.79 




















3 


0.80-0.89 








































































1 





In 10 min. 


































-' 










0.50-0.54 


2 


5 


2 


5 


3 


6 


10 


10 


7 


4 


4 


4 


3 


5 


4 


5 


2 


11 


3 


95 


329 


0.55-0.59 





6 


3 


4 


7 


3 


6 


5 


6 


4 


1 


3 


4 


2 





3 


2 


8 


2 


69 


234 


60-0.69 


2 


3 


5 


10 


5 


5 


3 


3 


11 


3 


7 


8 





6 


3 


8 


1 


3 


5 


91 


165 


0.70-0.79 


1 


1 


1 


3 


2 


1 


2 


2 


3 


2 


2 


5 


1 


2 





4 





2 


4 


38 


74 


0.80-0.89 





4 





1 


3 


2 








2 












2 











1 


1 


16 


36 


0.90-0.99 


1 




1 




1 




1 


1 


2 


1 


1 






1 





1 





1 


2 


14 


20 


1.00-1.09 


















1 




2 








1 




1 




1 


6 


6 





























In 15 min. 












































65-0.69 


1 


2 





4 


2 


3 


8 


5 


5 


1 


3 


5 





2 





2 





2 


4 


49 


268 


0.70-0.79 


2 


3 


5 


5 


6 


5 


7 


8 


4 


4 


4 


7 


3 


4 


2 


6 


4 


7 


5 


91 


219 


0.80-0.89 


1 


2 


1 


3 


3 


1 


1 


2 


11 


1 


5 


3 


4 


4 


2 


7 


2 


3 


2 


58 


128 


0.90-0.99 





2 


1 


1 


3 


2 


4 


2 


4 


2 





4 




3 











2 


4 


34 


70 


1.00-1.09 


1 


1 





3 


1 


2 




1 


4 





1 






1 














2 


17 


36 


1.10-1.19 




1 


1 




1 
















1 






1 





1 





1 


2 


9 


19 


1.20-1.39 












1 




1 


1 


1 



1 








1 


1 


1 


1 


1 


5 
1 


10 


1.40-1.59 


















1 











































In 30 min. 












































0.90-0.99 


2 


2 


2 


1 


5 


2 


5 


6 


6 


4 








1 


6 


6 


4 


2 


5 


7 


66 


250 


1.00-1.09 


1 


3 


3 


3 


4 


3 


8 


4 


5 


3 


2 


2 


1 


2 





4 





5 


6 


59 


184 


1.10-1.19 


2 


1 


2 


3 


5 





3 


3 


6 





2 


3 





2 


1 


3 


1 


2 


4 


43 


125 


1.20-1.39 





1 





2 


1 


3 


1 


5 


5 





4 


4 


2 


5 





2 


2 


4 


6 


47 


82 


1.40-1.59 


1 


1 


1 


1 





2 


1 


2 





2 


1 


1 


1 


1 





3 


1 





3 


22 


35 


1.60-1.79 









1 




1 


1 




1 



1 


1 



1 


1 











1 




1 




2 





1 


6- 

2 

3 

2 


13 


1 80-1.99 














7 


2.00-2.19 






















5 


2 20-2 39 


























2 









































PRECIPITATION 



157 



TABLE 11. — SUMMARY OF RECORDS OF INTENSE RAIN- 
STORMS AT FORTY-THREE STATIONS. — 1896-1914 — (Cont'd) 
Group No. 3 (317 Station-years) 





No. of storms of given intensity at 


Total 
No. of 
storms 
exceed- 
ing 
given 
inten- 
sity 


Precipita- 
tion in 60 
minutes 


d 





c 
< 






2. 
< 


"> 

X 



= 


2 
£ 




'3 
O 


c 
a 
s 


IS 

a 
5 
'S 
p 

5 


■d 

a 

O 


■0 

- 


-a c 

2 3 
OK 




3 

O 





-5 

S3 


3 
03 

Ph 
02 


■d 

c3 
<D 

-a 

u 

O 




"3 


0} 

il 

O 
Q 


"3 



1.20-1.29 


2 








1 





2 


3 


3 


1 


3 


3 


2 


3 


3 ! 


3 


2 


1 


5 


37 


175 


1.30-1.39 








1 


1 


2 


3 


2 


4 


2 





1 


2 


2 


3 





2 


1 


2 


5 


33 


138 


1.40-1.49 





2 


2 


1 





2 


3 


1 


2 


1 





1 





2 


1 


2 





3 


3 


26 


105 


1.50-1.59 


2 











2 





1 


3 


3 





1 





2 


1 





3 





1 


2 


21 


79 


1.60-1.79 


2 





2 


1 


1 





1 


1 


2 


1 


3 


2 




2 





1 


2 


3 


3 


27 


58 


1 80-1.99 




1 




1 





2 


1 


2 





P 














1 


1 


1 


1 


11 


31 


2.00-2.19 








1 
1 







1 








1 

11 


1 


1 




1 


1. 




1 

1 















1 
1 
1 




1 


1 
1 





1 


S 
4 
3 



1 

1 


20 


2.20-2.39 








12 


2 40-2.59 








8 


2.60-2.79 












2 80-2 99 
















^ 










3 


3.00-3.24 


































3 


3.25-3.49 
















, 


















>? 


3 50-3 74 






























1 










1 


1 





















In 100 min. 
1.30-1.39 
1.40-1.49 
1.50-1.59 
1.60-1.79 
1.80-1.99 
2.00-2.19 


3 

3 
1 
1 



1 



' 2 


2 
2 


2 


1 
1 

1 

1 
1 




1 


2 

1 
1 



1 



1 


3 
2 


3 


1 
2 
2 
1 
4 


4. 
1 


1 
3 
1 
1 
1 




1 


1 

2 
4 
2 
1 

1 



1 


p 

2 

2 

1 
1 
1 


1 


1 

2 


1 


1 
1 


1 

3 




2 


2 

2 


2 
2 

3 
1 



1 














1 

\ 


1 

2 
2 
2 
2 
1 
2 


1 


1 
1 
1 

1 

2 


3 
2 
1 
2 
3 
1 


7 
3 
1 
3 
-0 

1 
1 
1 

1 





1 


35 
25 
19 

24 
23 
8 
8 
3 
5 
2 
2 

1 


2 


157 
122 
97 
78 
54 
31 


2.20-2.39 








23 


2.40-2.59 








15 


2 . 60-2 . 79 








12 


2 80-2 99 








7 


3.00-3 24 


























3 25-3 49 
































3 


3.50-3.74 




































3.75-3.99 


































9 


4.00-4.49 




































2 


4.50-1.99 




































2 









































In 120 min. 
1.40-1.49 
1.50-1.59 
1.60-1 79 
1.80-1.99 
2.00-2.19 



3 
3 
1 


1 


2 


3 


2 


1 
1 
1 


1 
1 





1 



1 
1 







2 


2 


2 

1 


1 
3 

3 
1 

1 


1 

1 

1 
2 
1 
2 
1 




1 


2 
4 
1 
1 

1 
1 


1 


2 

1 
1 
1 
1 
1 




1 

2 

1 


1 



1 

2 
1 




2 



2 


2 

3 
1 


1 














1 


2 
2 
2 
2 
1 
2 




1 




1 

2 
2 


1 
2 
3 
1 


3 
1 
3 



2 


2 




1 


24 

21 

24 

21 

9 

7 

7 

5 

1 

4 



1 





2 


126 
102 
81 
57 
36 


2.20-2.39 








27 


2.40-2.59 








20 


2.60-2.79 








13 


2.80-2.99 








8 


3.00-3.24 
























7' 


3.25-3.49 


























3 


3.50-3.74 


































3 


3.75-3.99 


































2 


4.00-4.49 




































2 


4.50-4.99 




































2 









































158 



ELEMENTS OF HYDROLOGY 



TABLE 11.— SUMMARY OF RECORDS OF INTENSE RAIN- 
STORMS AT FORTY-THREE STATIONS — 1896-1914 — (Cont'd) 
Group No. 4 (73 Station-years) 



Precipitation 
in 5 minutes 



0.30-0.34 
0.35-0.39 
0.40-0.44 
0.45-0.49 
0.50-0.59 
0.60-0.69 
0.70-0.79 



No. of storms of given intensity at 



Duluth 



Escanaba Rochester 



Buffalo 



Total 



23 
13 

9 

1 

2 
1 

1 



In 10 minute? 
0.45-0.49 
0.50-0.59 
0.60-0.69 
0.70-0.79 
0.80-0.89 
0.90-0.99 
1.00-1.09 
1.10-1.19 
1.20-1.39 



In 15 minutes 

0.60-0.69 
0.70-0.79 
0.80-0.89 
0.90-0.99 
1.00-1.09 
1.10-1.19 
1.20-1.39 
1.40-1.59 



15 

18 
9 
8 

1 



1 



20 

11 

6 

4 
1 


1 
1 



In 30 minutes 














0.75-0.79 


3 


3 


3 


2 


11 


47 


0.80-0.89 


4 


5 


1 


2 


12 


36 


0.90-0.99 


2 





1 





3 


24 


1.00-1.09 


4 


1 


1 


2 


8 


21 


1 . 10-1 . 19 


1 





1 


3 


5 


13 


1.20-1.39 








1 


2 


3 


.8 


1.40-1.59 


2 










2 


5 


1.60-1.79 


1 


1 


1 




3 


3 


In 60 minutes 














0.90-0.99 


2 


4 


2 





8 


43 


1.00-1.09 


3 


3 


3 


1 


10 


35 


1 . 10-1 . 19 


1 


1 


1 


3 


6 


25 


1.20-1-29 


1 


1 


1 





3 


19 


1.30-1.39 


2 








2 


4 


16 


1.40-1.49 


2 











2 


12 


1.50-1.59 


1 





1 





2 


10 


1.60-1.79 


1 








1 


2 


8 


1.80-1.99 





1 


2 





3 


6 


2.00-2.19 
















3 


2.20-2.39 


1 







1 


2 


3 


2.40-2.59 






1 




1 


1 



PRECIPITATION 



159 



TABLE 11.— SUMMARY OF RECORDS OF INTENSE RAIN- 
STORMS AT FORTY-THREE STATIONS — 1896-1914 — (Cont'd) 
Group No. 4 (73 Station-years) 



Precipitation 


No. of storms of given intensity at 


Total No. of 
storms exceed- 


in 100 minutes 


Duluth 


Escanaba 


Rochester 


Buffalo 


Total 


ing given 
intensity 


1.00-1.09 


1 


3 


2 


1 


7 


40 


1.10-1.19 


3 


1 





3 


7 


33 


1.20-1.29 


1 


2 








3 


26 


1.30-1.39 


2 








2 


4 


23 


1.40-1.49 


2 





1 





3 


19 


1.50-1.59 


1 





2 





3 


16 


1.60-1.79 


1 





2 


1 


4 


13 


1.80-1.99 


1 


2 


2 





5 


9 


2.00-2.19 


1 










1 


4 


2.20-2.39 










1 


1 


3 


2.40-2.59 


1 









1 


2 


2.60-2.79 






1 




1 


1 



In 120 minutes 














1.10-1.19 


3 


1 





3 


7 


33 


1 20-1.29 


1 


1 








2 


26 


1.30-1.39 


2 








2 


4 


24 


1.40-1.49 


2 


1 


1 





4 


20 


1.50-1.59 


1 





2 





3 


16 


1.60-1.79 


1 








1 


2 


13 


1.80-1.99 





2 


3 





5 


11 


2.00-2.19 


2 




1 





3 


6 


2.20-2.39 










1 


1 


3 


2.40-2.59 


1 









1 


2 


2.60-2.79 






1 




1 


1 



Group No. 5 (38 Station-years) 



Precipitation in 5 minutes 


No. of storms of given intensity at 


Total No. of 
storms exceed- 


Denver 


Bismarck 


Total 


ing given 
intensity 


0.30-0.34 
0.35-0.39 
0.40-0.44 
0.45-0.49 
0.50-0.54' 
0.55-0.59 


3 
3 
3 

3 



1 


1 

5 
1 
1 

2 


4 

8 
4 
1 
5 



1 


23 
19 
11 


0.60-0.69 






0.70-0.79 






0.80-0.89 




1 









In 10 minutes 










0.45-0.49 


2 


5 


7 


33 


0.50-0.54 


7 


2 


9 


26 


0.55-0.59 


1 


2 


3 


17 


0.60-0.69 


1 


3 


4 


14 


0.70-0.79 


2 


3 


5 


10 


0.80-0.89 


2 





2 


5 


0.90-0.99 


1 


1 


2 


3 


1 00-1.09 




1 






1 


1 


1 . 10-1 . 19 




1 


1.20-1.39 




1 









160 



ELEMENTS OF HYDROLOGY 



TABLE 11. — SUMMARY OF RECORDS OF INTENSE RAIN- 
STORMS AT FORTY-THREE STATIONS — 1896-1914 — (Cmcl'd) 
Group No. 5 (38 Station-years) 



Precipitation 
in 15 minutes 


No. of storms of given intensity at 


Total No. of 
storms exceed- 


Denver 


Bismarck 


Total 


ing given 
intensity 


0.60-0.69 
0.70-0.79 
0.80-0.89 
0.90-0.99 
1.00 1.09 
1 . 10-1 . 19 
1.20-1.39 
1.40-1.59 


5 
2 
4 
2 
1 
1 

1 


5 
5 
2 
1 

1 


1 


10 

7 
6 
3 
2 
1 
1 
1 


31 

21 
14 
8 
5 
3 
2 
1 









In 30 minutes 










0.85-0.89 


o 
o 


1 


4 


26 


0.90-0.99 


2 


5 


7 


22 


1.00-1.09 


3 


3 


6 


15 


1.10-1.19 


1 


2 


3 


9 


1.20-1.39 


3 


1 


4 


6 


1.40-1.59 











2 


1.60-1.79 


1 





1 


2 


1.80-1.99 






1- 





1 


1 


2.00-2.19 




1 


2.20-2.39 




1 









In 60 minutes 










1.10-1.19 


2 


3 


5 


13 


1.20-1.29 


2 


2 


4 


8 


1 30-1.39 


1 


1 


2 


4 


1.40-1.59 











2 


1.60-1.79 


1 





1 


2 


1.80-1.99 










1 








1 


1 


2.00-2.19 




1 


2.20-2.39 




1 


2.40-2.59 




1 


2 . 60-2 . 79 




1 


2.80-2.99 




1 









In 100 minutes 

1.20-1.29 
1.30-1.39 
1.40-1.59 
1.60-1.79 
1.80-1.99 


o 

1 



1 


2 
1 

1 






1 


4 
2 

2 





1 


9 
5 
3 
3 


2.00-2.19 






2.20-2.39 






2.40-2.59 






2.60-2.79 






2.80-2.99 













In 120 minutes 

1.30-1.39 
1.40-1.59 
1.60-1.79 
1.80-1.99 


1 

1 


1 


1 





o 
1 


2 

2 






1 


5 
3 
3 


2.00-2.19 






2.20-2.39 






2.40-2.59 






2.60-2.79 






2.80-2.99 
















PRECIPITATION 



161 



TABLE 12. — DATA FOR 100 TYPICAL INTENSE RAIN- 
STORMS — 1896 — 1914 



Station 



Abilene, Texas, 
May 22, 1908 
Obs. precip. . . 

Increment 

Max. precip. . . 

Abilene, Texas, 
Oct. 22, 1908 
Obs. precip. . . 

Increment 

Max. precip. . . 

Abilene, Texas, 
July 31, 1911 
Obs. precip. . . 

Increment 

Max. precip. . . 

Anniston, Ala., 
Sept. 5, 1906 
Obs. precip. . . 

Increment 

Max. precip. . . 

Anniston, Ala., 
April 22, 1909 
Obs. precip. . . 

Increment 

Max. precip. . . 

Asheville, N. C 
Aug. 12, 1911 
Obs. precip. . . 

Increment 

Max. precip. . . 

Asheville, N. C 

June 12, 1914 

Obs. precip. . . 

Increment. . . 

Max. precip. . . 

Atlanta, Ga., 
July 23, 1898 
Obs. precip. . . 

Increment 

Max. precip. . . 

Atlanta, Ga., 
Mar. 15, 1912 
Obs. precip. . . 
Increment. .. 
Max. precip. . . 



Time in minutes 



5 10 15 20 25 30 35 40 45 50 60 



0.35 
0.35 
0.36 



0.06 
0.06 
0.35 



0.24 
0.24 
0.46 



0.29 
0.29 
0.65 



24 
0.24 
0.43 



0.38 
0.38 
0.38 



0.70 
0.70 
0.70 



0.27 
0.27 
0.40 



0.52 
0.17 
0.71 



0.16 
0.10 
0.65 



0.70 
0.46 
0.79 



0.86 
0.57 
1.24 



36 
0.12 

0.78 



0.75 
0.37 
0.75 



0.89 
0.19 

0.89 



0.82 
0.30 
1.04 



0.41 
0.25 

0.87 



1.03 
0.33 
1.12 



1.45 
0.59 

1.81 



0.64 
0.28 
1.06 



1.10 
0.35 
1.10 



0.91 
0.02 
0.91 



0.67 0.90 
0.40,0.23 
0.67 0.92 



0.13 0.25 
0.130.12 
0.490.68 



0.40 
0.15 
0.91 



1.06 
0.24 
1.35 



0.71 
30 
1.04 



1.36 
0.33 
1.45 



10 
0.65 
2.36 



1.07 
0.43 
1.31 



1.45 
0.35 
1.45 



0.94 
0.03 
0.94 



1.19 
0.29 
1.20 



0.63 
0.23 
1 14 



1.42 
0.36 
1.59 



0.80 
0.09 
1.22 



1.69 
0.33 

1.78 



2.65 
0.55 



1.42 
0.35 
1.59 



1.79 
0.34 
1.79 



1.02 
0.08 
1.02 



1.47 
0.28 
1.47 



0.86 
0.23 
1.29 



1.77 
0.35 

1.89 



0.89 
0.09 
1.38 



2.02 
0.33 



2.97 
0.32 
2.97 



1.67 
0.25 
1.73 



2.12 
0.33 
2.12 



1.09 
0.07 
1.09 



1.74 
0.27 
1.74 



1.05 
0.19 
1.41 



2.10 
0.33 

2.06 



1.05 
0.16 
1.54 



2.32 
0.30 
2.52 



3.25 
0.28 
3 . 25 



1.95 
0.28 
1.95 



2.40 
0.28 
2.40 



1.12 
0.03 
1.12 



1.85 
0.11 

1.85 



1.54 
0.49 
1.54 



2.41 
0.31 
2.41 



1.35 
30 
1.76 



2.76 
0.44 

2.77 



3.43 
0.18 
3.43 



2.09 
0.14 
2.09 



2.53 
0.13 
2.53 



2.56 
0.15 
2.56 



1.70 
0.35 
1.93 



3.01 
0.25 
3.01 



3.50 
0.07 
3.50 



2.17 
0.08 
2.17 



2.65 
12 
2.65 



1.9612.02 
0.1l|o.06 
1.96 2.02 



1.66 
0.12 
1.66 



1.78 
0.12 
1.86 



2 

0.04 
2.60 



1.92 
0.22 
2.11 



3.14 
0.13 
3.14 



3.56 
0.06 
3.56 



2.29 
0.12 
2.29 



2.67 
0.02 
2.67 



2.09 
0.07 
2.09 



1.88 
0.10 
2.01 



2.70 
0.10 
2.70 



2.27 
35 

2.27 



3.46 
0.32 
3.46 



3 60 
0.04 
3.60 



2.56 
0.27 
2.56 



2.29 
0.20 
2.29 



2.26 
0.38 
2.26 



3.17 
0.47 
3.17 



2.50 
0.23 
2.50 



3.65 
0.19 
3.65 



2.84 
0.28 



3.38 
1.09 
3.38 



0.52 

2.78 



100 120 



4 17 
1.00 
4.17 



3.29 
0.79 
3.29 



4 42 
0.25 
4.42 



3.94 
0.65 
3.94 



4.03 
0.65 
4.03 



4.32 
6.29 
4.32 



3.37 
0.59 
3.37 



162 



ELEMENTS OF HYDROLOGY 



TABLE 12. — DATA FOR 100 TYPICAL INTENSE RAIN- 
STORMS— 1896-1914— (Continued) 



No. 



10 



Station 



Atlanta, Ga., 
Aug. 20, 1914 

Obs. precip 

Increment 

Max. precip 

Atlantic City, N. J., 
May 31, 1906 

Obs. precip 

Increment 

Max. precip 

Augusta, Ga., 
June 18, 1911 

Obs. precip 

Increment 

Max. precip 

Baltimore, Md., 
Aug. 25, 1911 

Obs. precip 

Increment 

Max. precip 

Bentonville, Ark., 
April 23, 1908 

Obs. precip 

Increment 

Max. precip 

Birmingham, Ala., 
July 24, 1910 

Obs. precip 

Increment 

Max. precip 

Bismarck, N. D., 
Aug. 9, 1909 

Obs. precip 

Increment 

Max. precip 

Buffalo, N. Y.. 
Mar. 20, 1897 

Obs. precip 

Increment 

Max. precip 

Cairo, 111., 
June 28, 1905 

Obs. precip 

Increment 

Max. precip 

Cont. (50 min.+) 

Obs. precip 

Increment 

Max. precip 



Time in minutes 



5 10 15 20 25 30 35 40 45 50 60 80 100 120 



0.90 
0.40 
0.93 



1.19 
0.36 
1.19 



1 80 
1 24 
1.80 



75 
56 
1.11 



0.14 
0.06 
1.19 



0.57 
0.28 
0.74 



47 
33 
0.93 



0.16 
0.09 
0.70 

1.59 
0.27 
3.15 



1.02 
0.12 
1.22 



2.11 
o 31 
2 11 



1.30 
0.55 
1.55 



0.40 
0.26 
1.45 



0.86 
0.29 
1.03 



0.92 
0.45 
1.26 



0.22 
0.06 
0.94 

1.75 
0.16 
3.24 



1 33 
0.31 
1.56 



2.26 
0.15 
2.26 



1.74 

(I 4-1 
2 03 



1.04 
0.64 
1.62 



1.17 

ii :si 
i 31 



1.20 
0.28 
1.53 



0.26 
0.04 
1.17 

1.99 
0.24 
3.27 



1.67 
0.34 

1.87 



2.46 
0.20 
2.46 



2.22 
0.48 
2.22 



1.59 
0.55 
1.68 



1.60 
0.43 
1.60 



1.47 
0.27 
1.93 



0.30 
0.04 
1.43 

2.25 
0.26 
3.31 



1 96 
29 
2.01 



2.65 
0.19 
2.65 



2 30 
0.08 
2.30 



1.76 
0.17 
1.76 



1.87 
0.27 
1.87 



1.89 
0.42 
2.26 



0.34 
0.04 
1.67 

2.48 
0.23 
3.35 



2.44 2.89 3.03 
048l0.450.14 
2.44 2.893.03 



2.77 
0.12 

2.77 



1.81 
05 
1.81 



1.97 
0.10 
1.97 



2.40 
0.51 

2.58 



0.37 
0.03 
1.86 

2.72 
0.24 
3 39 



2 88 
(I 11 
2 88 



1.88 
0.07 
1.88 



1 99 
0.02 
1.99 



2.73 
33 

2.80 



0.46 
0.09 
2.02 

3.12 
0.40 
3.45 



2.01 
0.02 
2.01 



2.94 
0.21 
2.94 



0.71 
0.25 
2.29 

3.42 
0.30 
3.54 



3 19 
0.16 
3 19 



2 

(17 
2 



2 99 
0.05 
2.99 



1.05 
0.34 
2.56 

3.61 
0.19 
3.61 



2 23 
0.15 

2 23 



2.37 
0.14 
2.37 



PRECIPITATION 



163 



TABLE 12. — DATA FOR 100 TYPICAL INTENSE RAIN- 
STORMS — 1896-1914 — (Continued) 



Station 



Cairo, 111., 
July 30, 1913 

Obs. precip 

Increment 

Max. precip 

Chattanooga, Tenn. 
Aug. 17, 1912 

Obs. precip 

Increment 

Max. precip 

Chattanooga, Tenn. 
Aug. 22, 1912 
Obs. precip.. .).... 

Increment 

Max. precip 

Cincinnati, Ohio, 
May 20, 1902 

Obs. precip 

Increment 

Max. precip 

Cleveland, Ohio, 
Aug. 20, 1901 

Obs. precip 

Increment 

Max. precip 

Cleveland, Ohio, 
Aug. 29, 1903 

Obs. precip 

Increment. , 

Max. precip 

Columbia, Missouri 
June 29, 1909 

Obs. precip 

Increment 

Max. precip 

Concord, N. H., 
July 7, 1907 

Obs. precip 

Increment 

Max. precip 

Concordia, Kan., 
Aug. 26, 1908 

Obs. precip 

Increment 

Max. precip 



Time in'minutes 



5 10 15 20 25 30 35 40 45 50 60 80 100 120 



0.46 
0.46 
46 



0.25 
0.25 
0.45 



0.51 
0.51 

(i 51 



0.42 
0.42 
0.54 



37 
0.37 

0.67 



0.78 
0.78 
0.78 



0.14 
0.14 
0.36 



0.09 
0.09 
0.55 



10 
0.10 
0.53 



0.91 
0.45 
0.91 



0.48 
0.23 
0.75 



0.71 
0.20 
0.97 



0.75 
0.33 
0.96 



1.04 
0.67 
1.09 



1.04 
0.26 
1.04 



0.43 
0.29 
0.65 



0.30 
0.21 
1.06 



0.41 
0.31 

0.95 



1.32 

0.41 
1.32 



0.78 
0.30 
0.98 



0.78 
0.07 
1.26 



1.17 
0.42 
1.38 



1.46 
0.42 
1.46 



1.06 
0.02 
1.06 



0.79 
0.36 

0.87 



0.60 
0.30 
1.55 



0.83 
0.42 
1.37 



1.54 
0.22 
1.54 



1.66 
0.12 
1.66 



1.23 1.46 
0.4510.23 
1.32 1.62 



0.84 
0.06 
1.46 



1.71 
0.54 
1.71 



1.77 
0.31 
1.77 



1.09 
0.03 
1.09 



1.04 
0.20 
1.62 



2.13 
0.42 
2.13 



1.78 
0.01 
1.78 



1.17 
0.08 
1.17 



1.011. 24 
0.220.23 
1.10 1.34 



1.09J1 
0.4910.51 
1.88 2.18 



1.36 1.78 
0.530.42 
1.68 1.99 



1.761.85 
O.ioio.09 
1.76 1.85 



1.80 
0.34 
1.85 



1.33 
0.29 
1.68 



2.28 
0.15 
2.28 



1.44 
0.20 
1.63 



2.15 
0.55 
2.39 



2.09 
0.31 
2.13 



2.10 
0.30 
2.10 



1 84 
0.51 
! 84 



2.30 
0.02 
2.30 



1.77 
0.33 

1.77 



2.48 
0.33 
2.60 



2.23 
0.14 

2.25 



2.22 
0.12 
2.22 



2.30 
0.46 
2.30 



1.88 
0.11 

1.88 



2.69 
0.21 

2.69 



2.27 
0.05 

2.27 



2 46 
0.16 
2.46 



2.02 2.30 
0.140.28 
2.16 2.38 



2.35 2.43 
0.12 0.08 
2.35 2.43 



2.73 
0.43 
2.73 



0.11 

2.84 



164 



ELEMENTS OF HYDROLOGY 



TABLE 12. — DATA FOR 100 TYPICAL INTENSE RAIN- 
STORMS — 1896-1914 — (Continued) 



No. 



28 



29 



30 



33 



:>4 



3:. 



36 



Station 



Dallas, Texas, 

Sept. 22, 1914 

Obs. precip. . 

Increment. . . 

Max. precip. . 



Davenport, Iowa, 
July 14, 1910 

Obs. precip 

Increment 

Max. precip 



Del Rio, Texas, 

July 2, 1914 

Obs. precip.. . 

Increment.. . . 

Max. precip. . . 



Denver, Colo.. 

July 14, 1912 

Obs. precip. . 

Increment. . 

Max. precip. 



Des Moines, Iowa, 
July 15, 1907 

Obs. precip 

Increment 

Max. precip 



Dodge City, Kan. 
Sept. 16, 1906 

Obs. precip 

Increment 

Max. precip 



Dodge City, Kan., 
July 17, 1911 

Obs. precip 

Increment 

Max. precip 



Duluth, Minn., 

July 21, 1909 

Obs. precip. . 

Increment. . . , 

Max. precip. . . 



Duluth, Minn., 
Aug. 12, 1910 
Obs. precip. . . 

Increment 

Max. precip. . . 



Time in minutes 



5 10 15 20 25 30 35 40 45 50 60 80 100 120 



0.07 
07 
0.62 



0.38 
38 
0.54 





0.08 

0.28 



0.32 
0.32 

0.87 



0.11 
0.11 
0.35 



0.35 
0.35 
0.47 



0.15 
0.15 
0.5f 



0.05 
0.05 
0.41 



0.16 
0.16 
0.52 



0.41 
0.34 
0.96 



0.92 
0.54 
1.00 



0.18 
0.10 
0.48 



0.75 
0.34 
1.30 



1.38 
0.46 
1.38 



0.36 
0.18 
0.68 



1.19 
0.87 
1.20 



0.28 
0.17 
0.68 



71 
0.36 
0.91 



1.52 
(I 33 
1 52 



0.50 
0.22 
0.91 



0.96 
25 
1.25 



0.28 0.39 
0.130.11 
1.02 1.16 



14 
0.09 
0.75 



0.62 
0.46 
0.98 



0.31 
0.17 
1.06 



1.14 
0.52 
1.22 



1.37 
0.62 
1.49 



1 59 
0.21 
1.59 



0.56 
20 

0.88 



1.56 
0.19 
1.72 



1.61 
0.02 
1.61 



0.84 
0.28 



62 
0.10 
1.62 



0.85 
0.35 
1.13 



1.30 
0.34 
1.54 



0.90 
0.51 
1.27 



0.22 
1.28 



1.67 
0.05 
1 67 



1.79 
0.23 
1.81 



1.62 
0.01 
1.62 



0.99 
0.15 
1.28 



1.72 
0.05 
1.72 



1.38 
0.24 
1.38 



1.18 

33 

1 34 



1.77 
0.47 
1.86 



1 41 
0.51 
1.40 



0.34 
1.45 



1.40 
0.02 
1.40 



1.73 
0.11 
1.73 



1.10 
0.11 

1.48 



1.82 
09 
1.82 



1.32 
0.22 
1.61 



1.45 
0.13 

1.83 



0.23 
1.52 



2.21 
0.44 
2.21 



1 55 
0.14 
1.55 



1.28 
0.41 
1.60 



o 21 
1.69 



2.50 
0.29 
2.50 



1.63 
0.08 
1.63 



1.59 
0.31 
1.71 



1 

0.18 
1 



2.81 
(i 31 

2 SI 



1.66 
0.03 
1.66 



1.74 
0.15 
1.80 



1.90 
0.10 
1.90 



2.95 
0.14 
2.95 



1.71 

0.05 
1.71 



1.85 
0.11 
1.96 



1.65 
0.20 
1.94 



2.13 
0.48 
2.37 



2 01 
0.11 

2 01 



3.11 
0.16 
3.11 



1.79 
0.08 
1.79 



1.94 
0.09 
2.12 



2.93 3.31 
0.800.38 
2.93 3.31 



2.14 
0.13 
2.14 



3.47 
0.36 
3.47 



1.93 
0.14 
1.93 



2.26 
0.32 
2.26 



2.95 3.29 
0.810.34 
2.95 3 29 



4.27 
0.80 
4.27 



2.51 

0.58 

51 



2 51 
0.25 
2.51 



3 56 
0.25 
3 56 



4.85 
0.58 

4.85 



2.73 
0.22 
2.73 



3.12 
0.39 
3 12 



PRECIPITATION 



165 



TABLE 12. — DATA FOR 100 TYPICAL INTENSE RAIN- 
STORMS — 1896-1914— {Continued) 



Station 



Elkins, W. Va., 
Aug. 4, 1911 

Obs. precip 

Increment 

Max. precip 

Escanaba, Mich., 
July 12, 1903 

Obs. precip 

Increment 

Max. precip 

Evansville, Ind., 
Aug. 10, 1908 

Obs. precip 

Increment 

Max. precip 

Ft. Worth, Texas, 
Sept, 21, 1900 

Obs. precip 

Increment 

Max. precip 

Galveston, Texas, 
April 22, 1904 

Obs. precip 

Increment 

Max. precip 

Cont. (50 min.+) 

Obs. precip 

Increment 

Max. precip 

Cont. (100 min.+) 

Obs. precip 

Increment 

Max. precip 

Galveston, Texas, 
Oct. 6, 1910 

Obs. precip 

Increment 

Max. precip 

Galveston, Texas, 
Oct. 22, 1913 

Obs. precip 

Increment 

Max. precip 

Grand Rapids, Mich., 
June 26, 1909 

Obs. precip 

Increment 

Max. precip 



Time in minutes 



0.34 
0.34 
0.42 



0.10 
0.10 
0.69 



0.70 
0.36 
0.78 



0.79 
0.69 
1.32 



0.12 0.30 
0.120.18 
0.48 0.82 



0.15 
0.15 

0.46 



0.75 
0.22 
0.51 

3 59 
0.26 
4.15 

7 46 
0.33 
6.99 



0.17 
0.17 

0.48 



0.38 
0.38 
0.65 



0.36 
0.36 
0.48 



0.42 
0.27 
0.83 



1.04 
0.29 
0.94 

3.99 
0.40 
4.41 

7.74 
0.28 
7.21 



0.36 
0.19 




1.03 
0.65 
1.19 



0.84 

0.48 
0.84 



0.94 
0.24 
1.02 



1.42 
0.63 
1.52 



50 
0.20 
1.15 



79 
0.37 
1.10 



1.39 
0.35 
1.38 

4.50 
0.51 
4.67 

7.95 
0.21 

7.42 



0.58 
0.22 
1.44 



1.57 
0.54 
1.58 



1.10 
0.26 
1.10 



1.36 
0.42 
1.38 



1.62 
0.20 
1.62 



0.71 
0.21 
1.36 



1.07 
0.28 
1.38 



1 72 
0.33 

1.88 

4.93 
0.43 
4.97 

8.11 
0.16 

7.58 



0.94 
0.36 
1.92 



1.92 
0.35 
2.02 



1.31 
0.21 
1 31 



1.72 
0.36 
1.72 



1.65 
0.03 
1.67 



1.05 
0.34 
1.56 



1 34 
0.27 
1.75 



1.92 
0.20 

2.28 

5.37 
0.44 
5.19 

8.26 
0.15 
7.73 



1.22 
0.28 
2.37 



2 17 
0.25 
2.45 



1.51 

0.20 
1.51 



1.95 
0.23 
1.95 



1.77 1.87 
0.12 0.10 

1.77 1.87 



1.53 1.86 
0.4810.33 
1.75 1.95 



1.80 2.17 
0.460.37 
2.02 2.25 



2.11 
0.16 
2.11 



2.18 
0.26 
2.67 

5.87 
0.50 
5.56 

8.36 
0.10 

7.83 



1.47 
0.25 
2.82 



2 60 
0.43 
2.80 



1.71 
0.20 
1.71 



2.55 
0.37 
2.94 

6.26 
0.39 
5.82 



1.74 
27 
3.27 



3 04 
0.44 
3.14 



1.86 
0.15 
1.86 



2.22 
0.11 

2.22 



1.90 
0.03 
1.90 



2.01 
0.15 
2.15 



2.40 
0.23 

2.48 



2.77 
0.22 
3.27 

6.53 
0.27 
6.03 



1.83 
0.09 
3.72 



3.63 
0.59 
4.69 



2.01 
0.15 
2.01 



2.28 
0.06 

2.28 



2.25 
0.24 
2.33 



2.63 
0.23 
2.66 



3.07 
0.30 
3.54 

6.86 
0.33 
6.35 



1.89 
06 
3.81 



4.07 
0.44 
4.24 



2.11 
0.10 
2.11 



2.32 
0.04 
2.32 



2.45 
0.20 
2.45 



2.81 
0.18 
2.81 



3.33 
0.26 

3.87 

7.13 

0.27 
6.70 



2.50 
0.05 
2.50 



2.09 
0.20 
3.90 



4.62 
0.55 
4.62 



2.19 
0.08 
2.19 



inn 



L20 



3.08 3.66 
0.27 0.58 
3.08 3.66 



2.27 
0.18 
4.16 



5.31 
0.69 
5.31 



4.07 
1.80 
5.05 



6 02 
0.71 
6.02 



3.95 
0.29 
3.95 



4.32 
0.37 
4.32 



5.99 
1.92 
5.99 



6.28 
0.29 

6.28 



6.52 
0.50 
6.52 



166 



ELEMENTS OF HYDROLOGY 



TABLE 12. — DATA FOR 100 TYPICAL INTENSE RAIN- 
STORMS — 1896-1914 — (Continued) 



No. 



45 



48 



49 



Station 



Green Bay, Wis. 
Aug. 9, 1906 
Obs. precip. . . . 

Increment 

Max. precip 



Hannibal, Mo. 

July 29, 1910 

Obs. precip. . 

Increment. . . 

Max. precip. . 



Houghton, Mich;, 
Sept. 7, 1913 

Obs. precip 

Increment 

Max. precip 

Cont. (50 min.+) 

Obs. precip 

Increment 

Max. precip 

Cont. (100 min.+) 

Obs. precip 

Increment 

Max. precip 

Indianapolis, Ind., 
Aug. 13, 1913 

Obs. precip 

Increment 

Max. precip 



Indianapolis, Ind. 
Sept. 30, 1902 
Obs. precip. 

Increment 

Max. precip 



Jacksonville, Fla. 
Aug. 16, 1901 

Obs. precip 

Increment 

Max. precip 



Jacksonville, Fla. 
Sept. 6, 1907 

Obs. precip 

Increment 

Max. precip 



Jupiter, Fla., 
Oct. 28, 1908 
Obs. precip.. 
Increment. . 
Max. precip. 



Time in minutes 



5 10 15 20 25 30 35 40 45 50 60 



0.23 
0.23 
0.37 



32 
0.32 
0.35 



0.21 
0.21 
0.31 

2.21 
0.11 
2.45 

3.95 
0.15 
3.95 



0.24 
0.24 
0.51 



0.39 
0.39 
69 



0.11 

0.11 
0.72 



36 
0.36 
0.52 



0.31 
0.31 
54 



0.60 
0.37 
0.69 



0.67 
0.35 
0.67 



0.44 
0.23 
0.57 

2.52 
0.31 
2.61 

4.08 
0.13 

4.08 



0.50 
0.26 
0.96 



1.08 
0.69 
1.08 



0.83 
0.72 
0.89 



0.66 
0.30 
0.99 



62 
0.31 
1.07 



0.92 
0.32 
1.06 



0.84 
0.17 

0.84 



0.53 
0.09 
0.84 

2.71 
0.19 
2.76 

4.16 
0.08 
4.16 



0.95 
0.45 
1.28 



1.09 
0.01 
1.09 



1.00 
0.17 
1.00 



1.18 
0.52 
1.42 



0.88 
26 
1.54 



1.29 
0.37 
1.36 



0.86 
02 
0.98 



0.68 
0.15 
1.09 

2.94 
0.23 
2.86 

4.28 
0.12 

4.28 



1.46 
0.51 
1.54 



1.10 
0.01 
1.10 



1.59 
0.30 
1.59 



0.89 
0.03 
1.12 



0.84 
0.16 
1.26 

3.04 
0.10 

3.08 



1.78 
0.32 
1.78 



1.08 1.22 
0.08 0.14 
1.11 1.22 



1.65 2.08 
0.4710.43 
1.72 2.08 



1.35 1.63 
0.47 0.28 
1.822.29 



1.81 
0.22 
1.81 



0.93 
0.04 
1.26 



111 

0.27 
1.42 

3.29 
0.25 
3.29 



1.98 
0.20 
1.98 



1.28 
0.06 
1.28 



2.29 
0.21 

2.29 



2.10 
0.47 
2.55 



2.03 
0.22 
2.03 



0.95 
0.02 
1.41 



1.38 
0.27 
1.68 

3.39 
0.10 
3.38 



2.05 
0.07 
2.05 



2.08 
0.05 
2.08 



1.19 
0.24 
1.55 



1.68 
0.30 

1.87 

.3.49 
0.10 
3.49 



2.18 
0.13 
2.18 



0.20 
2.49 



0.24 
2.73 



2.64J3.17 
0.54J0.53 
2.86 3.17 



1.54 
0.35 
1.70 



1.93 
0.25 
2.10 

3.65 
0.16 
3.65 



2.41 
0.23 
2.41 



2.85 
0.12 
2.85 



3.40 
0.23 
3.40 



1.79 
0.25 
1.86 



2.10 
0.17 
2.26 

3.80 
0.15 
3.80 



2.56 
0.15 
2.56 



2 93 

DOS 



3 66 
0.26 
3.66 



2.07 
0.28 
2.17 



2.66 
0.10 
2.66 



3.83 
0.17 
3.83 



2.65 
0.58 

2.77 



2.80 
0.14 
2.80 



4.15 

0.32 

15 



100 120 



3.27 3.87 
0.62 0.60 
3.27 3.87 



4.41 
26 
4.41 



4.59 
0.18 
4.59 



PRECIPITATION 



167 



TABLE 12. — DATA FOR 100 TYPICAL INTENSE RAIN- 
STORMS — 1896-1914 — (Continued) 



Station 



Kansas City, Mo., 
May 31, 1896 

Obs. precip 

Increment 

Max. precip 



Kansas City, Mo., 
Aug. 23, 1906 

Obs. precip 

Increment 

Max. precip 



Kansas City, Mo., 
Sept. 15, 1914 

Obs. precip 

Increment 

Max. precip. . . 



Knoxville, Tenn. 
Aug. 4, 1905 
Obs. precip. . . . 

Increment 

Max. precip. . . . 



Lincoln, Neb. 

May 27, 1914 

Obs. precip. . 

Increment . . 

Max. precip. 



Lincoln, Neb., 
June 5, 1914 

Obs. precip 

Increment 

Max. precip 

Cont. (50 min.+) . 

Obs. precip 

Increment 

Max. precip 

Cont. (100min.+). 

Obs. precip 

Increment 

Max. precip 



Lincoln, Neb. 

July 25, 1914 

Obs. precip. . 

Increment . . 

Max. precip. 



Lynchburg, Va., 
June 24, 1905 
Obs. precip. 
Increment 
Max. precip. . . . 



Time in minutes 



5 10 15 20 25 30 35 40 45 50 60 80 100 120 



0.80 
0.80 
0.80 



22 
0.22 
0.57 



19 
0.19 
0.55 



0.08 
08 
0.46 



28 
0.28 
0.44 



0.05 
0.05 
0.35 

2.20 
0.13 
2.43 

3.03 
10 
3.03 



0.29 
0.29 
62 



0.19 
0.19 
0.56 



1.05 
0.25 
1.05 



0.60 
38 
1.12 



0.35 
0.16 
1.09 



0.13 
0.05 
0.88 



0.72 
0.44 
0.72 



0.14 
0.09 
0.64 

2.32 
0.12 
2.66 

3.26 
0.23 
3.26 



0.72 
0.43 
1.16 



0.58 
0.39 
1.03 



1.02 
0.42 
1.65 



0.47 
0.12 
1.57 



0.23 
0.10 
1.24 



0.96 
0.24 
1.03 



0.35 
0.21 
0.94 

2.57 
25 
2.76 

3.35 
0.09 
3.35 



1.26 
0.54 
1.59 



1.14 
0.56 
1.42 



1.52 
0.50 
2.15 



0.68 
0.21 

1.85 



0.29 
0.06 

1.48 



1 31 
35 
1.31 



0.65 
0.30 
1.23 

2.80 
0.23 

2.85 

3.40 
0.05 
3.40 



1 

0.62 
1 



1.61 
0.47 
1.66 



2 02 

0.50 

65 



0.91 
23 
2.08 



0.41 
0.12 
1.60 



1 53 
0.22 
1.61 



0.94 
0.29 
1.46 

2.90 
0.10 
2.90 

3.57 
0.17 

3.57 



2.18 
0.30 
2.24 



1.85 
0.24 
1.85 



2.57 
0.55 
3.07 



1.19 
0.28 
2.29 



0.83 

42 

1 70 



1.89 
0.36 
1.89 



1.29 
0.35 
1.67 

2.92 
0.02 
2 92 

3.61 
0.04 
3.61 



2.53 
0.35 
2.53 



2.04 
19 
2.04 



3.14 
0.57 
3.45 



1.74 
0.55 
2.43 



1 29 
0.46 
1.76 



2 07 
0.18 
2.11 



1.58 
0.29 
1.79 

2.92 
00 
2.92 



2.78 
0.25 

2.78 



2.19 
0.15 
2.19 



3.67 
0.53 
3.79 



2.28 
0.54 
2.57 



4.01 
34 
4.10 



2.76 
0.48 

2.76 



1.65 1.89 
0.36 0.24 
1.86 1.91 



2 39 
0.32 
2.39 



1.81 
0.23 
1.93 

2.93 
0.01 
2.93 



2.47 
0.08 
2.47 



1.93 
0.12 
2.06 

2 93 
00 
2.93 



2.90 
0.12 
2.90 



2.25 
0.06 
2.25 



2.31 
0.06 
2.31 



4 32 
() 31 
4.32 



2.90 
0.14 
2.90 



1.99 
0.10 
1.99 



2.72 
0.25 

2.72 



2.07 
0.14 

2.18 

2.93 
0.00 
2.93 



3.06 
0.07 
3.06 



4.74 

0.42 

74 



2.93 
0.03 
2.93 



5.45 
0.71 
5.45 



3 41 
48 
3 41 



5.74 
0.29 
5.74 



3 51 
0.10 
3.51 



168 



ELEMENTS OF HYDROLOGY 



TABLE 12. — DATA FOR 100 TYPICAL INTENSE RAIN- 
STORMS — 1896-1914 — (Continued) 



No. 



(I.-. 



m 



Station 



Lynchburg, Va., 
Sept. 3, 1907 

Obs. precip 

Increment 

Max. precip.. 

Madison, Wis., 
Aug. 8, 1906 

Obs. precip 

Increment 

Max. precip 

Marquette, Mich., 
June 23, 1907 

Obs. precip 

Increment 

Max. precip 

Memphis, Tenn., 
March 9, 1901 

Obs. precip 

Increment 

Max. precip 

Meridian, Miss., 
Aug. 13, 1906 

Obs. precip 

Increment 

Max. precip 

Miami, Fla., 
Nov. 8, 1914 

Obs. precip 

Increment 

Max. precip 

Minneapolis, Minn., 
Aug. 22, 1914 

Obs. precip 

Increment 

Max. precip 

Montgomery, Ala., 
May 30, 1905 

Obs. precip 

Increment 

Max. precip 

Moorhead, Minn., 
Aug. 29, 1908 

Obs. precip 

Increment 

Max. precip. 



Time in minutes 



5 10 15 20 25 30 35 40 45 50 60 



025 
0.25 
0.42 



0.21 
0.21 
0.55 



0.29 
0.29 
35 



0.78 
0.78 
0.78 



0.17 
0.17 

0.56 



0.10 
10 
0.37 



0.30 
0.30 
0.53 



0.08 
0.08 
0.54 



0.34 
0.34 
0.68 



0.34 
0.09 
82 



74 
0.53 

1.08 



0.53 
0.24 
0.68 



92 
0.14 

0.92 



0.38 
0.21 
1.05 



0.46 
0.36 
0.73 



0.57 
0.27 
0.90 



0.17 
0.09 
1.04 



1.02 

0.68 
1.02 



0.56 
0,22 
1.22 



1 29 
0.55 
1.37 



0.59 
0.06 
0.95 



97 
0.05 
0.97 



0.76 
0.38 
1.52 



0.83 
0.37 
1.06 



0.83 
0.26 
1.12 



0.36 
0.19 
1.41 



1.24 
0.22 
1.24 



0.94 1.30 
0.38 0.36 
1.47 1.61 



1.58 1.82 
0.29 0.24 
1.61 1.88 



0.75 1.02 
0.160.27 
1.16 1 42 



1.02 
0.05 
1.02 



1.05 
0.03 
1.05 



1.61 
0.31 

1 88 



2.09 
0.27 
2.09 



1.35 
0.33 
1.67 



1.25 1.81 2.28 
49 0.56 47 
1.902.15 2.36 



1.16 1.47 
0.33 0.31 
1.37 1.67 



1.03,1 40 
0.20|0.37 
1.36-1.63 



0.70,1.08 
0.34;0.38 
1.78 2.15 



1.28 1.33 
0. 0410.05 
1.28 1.33 



1.77 
0.30 
1.94 



1.93 

0.53 
1.93 



1.44 
0.36 
2.49 



1.34 
0.01 
1.34 



2.29 
0.20 
2.,29 



1 70 
0.35 
1.92 



2 53 
0.25 

2.56 



2 04 
0.27 
2.13 



2.15 
0.22 
2.15 



1.98 
0.54 

2.68 



1.35 
0.01 
1.35 



2.02 
14 
2.55 



2.50 
0.21 
2.50 



1.91 
0.21 

2.18 



2.73 
0.20 
2 73 



2 23 
0.19 

2.26 



2.21 
0.06 
2.21 



2.48 
0.50 



1.38 
0.03 
1.38 



2.27 
0.25 
2.93 



2.85 
35 

2.85 



2.17 
26 
2.34 



2.89 
0.16 

2.89 



2 36 
0.13 
2.46 



2.85 
0.37 
3.10 



1.40 
0.02 
1.40 



2 69 
42 

3 15 



3.19 
0.34 
3.19 



3.61 4 54 
0.42 93 
3.61 4.54 



2.42 2.93 
0.25 0.51 
2.49 2.93 



3.06 
0.17 
3.06 



2.56 
0.20 
2.66 



3.03 
0.18 
3.29 



1.40 
0.00 
1.40 



3.63 

57 
3.63 



2.96 
40 
2.99 



3.46 
0.43 
3.46 



1.72 
0.32 
1.72 



3 54 
61 
3.54 



.'! . 71 
0.11 
3.74 



4.84 
30 
4.84 



3.48 3 
0.52 0.42 

3.49 3.97 



1.98 
0.26 
1.98 



4 59 
0.69 
4.59 



PRECIPITATION 



1G9 



TABLE 12. — DATA FOR 100 TYPICAL INTENSE RAIN- 
STORMS — 1896-1914— (Continued) 



Station 



New Orleans, La., 
Sept. 30, 1905 

Obs. precip 

Increment 

Max. precip 

New York City, N. Y., 

July 10, 1905 

Obs. precip 

Increment 

Max. precip 

New York City (Bor- 
ough of Richmond) 
Oct. 1, 1913 

Obs. precip 

Increment 

Max. precip 

Norfolk, Va., 
Aug. 14, 1898 

Obs. precip 

Increment 

Max. precip 

Oklahoma, Okla., 
June 23, 1908 

Obs. precip 

Increment 

Max. precip 

Pensacola, Fla., 
Sept. 29, 1906 

Obs. precip 

Increment 

Max. precip 

Cont. (50 min.+) 

Obs. precip 

Increment 

Max. precip 

Cont. (100 min.+) 

Obs. precip 

Increment 

Max. precip 

Cont. (150min.+) 

Obs. precip 

Increment 

Max. precip 

Pensacola, Fla., 
Oct. 20, 1909 

Obs. precip 

Increment 

Max. precip 



29 
29 
0.60 



43 
43 
68 



Time in minutes 



5 10 15 20 25 30 35 40 45 50 60 



0.22 
0.-22 
0.36 



0.10 
0.10 
42 



0.49 



0.05 
0.05 
0.80 



78 

49 

1 19 



95 
0.52 
1.20 



0.20 
0.20 
85 



o 45 
23 
67 



0.17 
0.07 




0.76 
0.41 
0.87 

3.82 
0.25 
3.82 

5.90 
24 
5.90 

6.81 

0.09 
6.81 



1.38 
60 
1.68 



1 63 
0.68 
1 63 



0.12 
0.07 
1.53 



1 97 

59 

1 97 



67 
22 
89 



0.28 
0.11 
1 08 



1.13 
0.37 
1.24 

4.02 
0.20 
4.02 

6.10 
0.20 
6.10 



0.26 
0.14 

2.29 



48 
28 
1.60 



1 03 
36 
1.12 



0.47 
0.19 
1.40 



1.62 
0.49 
1.65 

4.16 
0.14 
4.16 



2 23 
26 
2.23 



2 37 
14 
2.37 



0.11 0.09 
1.99 2.08 



1.00 

52 

40 



1.34 
31 
1.34 



0.79 
0.32 
1.68 



2 00 
0.38 
2.00 

4.28 
0.12 

4.28 



6.24 6.27 
0.14 0.03 
6.24 6.27 



0.33 
0.07 

2.88 



0.92 
0.59 
3.37 



2.45 
08 
2 45 



2 11 
03 
2 11 



1 56 
22 
1.56 



1.07 
0.28 
1.93 



1.72 
0.80 
3.65 



1.72 
0.16 
1.72 



1 45 
0.38 

2 12 



2.53 
0.23 
2.53 

4.6 

0.26 

4.67 

6.28 
0.00 
6.28 



2.45 
0.73 

3.79 



1.75 
75 
3.15 



1.84 2.04 2.14 
0.12 0.20 0.10 
1.84J2.04J2.24 



2 60 
0.85 
3.70 



1.87 2.15 
0.42J0.28 
2.25 2.37 



793 
26 0. 
79 3. 

5. 

22J0. 
89J5. 

336. 
05 0. 
33 6. 



3.21 
0.76 
3.94 



3.70 
0.49 
4.01 



40 
25 



3 35 
27 
3.35 



5 33 
0.25 
5.33 

6 63 
0.16 
6.63 



3 

0.28 

4.15 



3 30 
70 
4.22 



2 69 
55 



2.65 
25 
2.65 



4.27 
0.29 
4.27 



4.70 
0.55 

17 



2.59 
90 
3.59 



4.49 
0.22 
4.49 



100 102 



5 65 
0.45 

5.72 



4.44 
0.85 
4.44 



6.20 
0.40 
6.20 



4.73 

29 
4.73 



4.73 
0.24 
4.73 



4.82 
0.09 

4.82 



170 



ELEMENTS OF HYDROLOGY 



TABLE 12. — DATA FOR 100 TYPICAL INTENSE RAIN- 
STORMS — 1896-1914 — (Continued) 



No. 



Station 



Philadelphia, Pa. 
Aug. 6, 1905 

Obs. precip 

Increment 

Max. precip. . . . 



82 



83 



84 



Raleigh, N. C. 
July 14, 1914 

Obs. precip. 

Increment . . 

Max. precip.. 



Richmond, Va., 
Aug. 19, 1908 

Obs. precip 0.40 

Increment 0.40 

Max. precip 0.70 



Time in minutes 



5 10 15 20 25 30 35 40 45 50 60 80 100 120 



11 
11 
0.49 



0.22 
0.22 
73 



Rochester, N. Y., 
July 11,. 1897 

Obs. precip 

Increment 

Max. precip 



0.29 
18 
94 



0.56 
0.34 
1 35 



86 

46 

1 13 



St. Louis, Mo., 
March 4, 1897 
Obs. precip. . . 

Increment 

Max. precip. . . 



St. Louis, Mo. 

May 1, 1898 

Obs. precip. . 

Increment. . 

Max. precip. 



0.14 
0.14 
0.35 



0.88 
0.88 
0.88 



0.27 
0.27 
0.74 



St. Louis, Mo., 
July 14, 1912 
Obs. precip. . . 

Increment 

Max. precip. . . 

St. Paul, Minn. 

Aug. 9, 1902 

Obs. precip. . . 

Increment... . 

Max. precip. . . 



Sandusky, Ohio, 
Aug. 7, 1906 

Obs. precip 

Increment 



44 
0.30 
65 



93 
05 
0.93 



43 
0.16 
79 



55 
0.26 

1 35 



86 
30 
1.71 



1.14 
28 
1.46 



71 
0.27 
99 



0.96 1 45 
0.410.49 
1.61 1 81 





0.05 

0.98 



0.48 
0.05 
0.95 



0.14 0.41 
0.14 0.27 
0.40 0.70 



0.06 
0.06 
0.45 



0.26 
0.26 



Max. precip 0.56 



0.12 
0.06 
0.90 



0.49 
0.23 
0.85 



1 48 
62 

2 01 



1.57 
0.43 
1 87 



1 06 
35 
1.26 



0.99 
0.01 
99 



1.22 
0.74 
1.22 



2.21 

0.73 
2 35 



2.27 
70 
2 27 



1.36 

30 

1 56 



0.72 
0.31 
0.98 



0.33 
0.21 
1.31 



0.78 
0.29 
1.10 





0.27 

1.20 



1.00 
0.01 
1.00 



1.23 
0.01 
1.23 



1.18 
0.19 
1.43 



1.90 
45 
1.97 



2 57 
0.36 

57 



2 60 
33 
2 60 



1 70 
34 

1.70 



1.03 
03 
1.03 



1.24 
0.01 
1.24 



0.71 1.12 
0.38 0.41 
1.69 1.90 



1.34 
0.56 
1.33 



1.59 
0.25 
1 59 



10 

20 

10 



2.76 
0.19 

2.76 



69 

09 

69 



1 

14 
1 



1.05 
0.02 
1.05 



2 19 
0.09 
2.19 



2 87 
0.11 
2 87 



2 75 
0.06 
2.75 



1 

12 
1 



1.06 
0.01 
1.06 



2 32 

0.13 

32 



2 94 
07 
2 94 



2 85 
10 

2.85 



2.12 
16 
2 12 



1.09 
03 
1.09 



1.30 1.58 
12 0.28 
1.65 1.87 



1.57 
0.45 
2.06 



1.74 
0.15 
1.74 



1.98 
40 
2 14 



2.02 
0.45 
2.15 



1.98 
24 
1.98 



2 99 
05 



91 
06 
2 91 



2 24 

12 
2 24 



1 14 
0.05 
1.14 



2 28 2.50 
0.30 0.22 
2.36 2.58 



2.49 
0.25 
2.49 



1 23 



1.23 



2.182.272.38 
0. 16|6.09 0.11 
2.26 2.32 2.39 



2.11 
0.13 
2.11 



2.16 
0.05 
2.16 



2.95 
45 
2.95 



2.51 
0.13 
2.51 



2.22 
0.06 
2.22 



2 74 
0.25 
2.74 



1.36 
0.13 
1.36 



3.07 
0.12 
2.07 



2.9313.04 
.180.240.11 
2.93 3.04 



PRECIPITATION 



171 



TABLE 12. — DATA FOR 100 TYPICAL INTENSE RAIN- 
STORMS — 1896-1914 — (Continued) 



Station 



Shreveport, La., 
July 23, 1905 

Obs. precip 

Increment 

Max. precip 

Cont. (50 min.+) 

Obs. precip 

Increment 

Max. precip 

Cont. (100+) 

Obs. precip 

Increment 

Max. precip 

Cont. (150 min.+) 

Obs. precip 

Increment 

Max. precip 

Springfield, 111., 
July 6, 1912 

Obs. precip 

Increment 

Max. precip 

Tampa, Fla., 
June 20, 1905 

Obs. precip 

Increment 

Max. precip 

Taylor, Texas, 
Apr. 29, 1905 

Obs. precip 

Increment 

Max. precip 

Taylor, Texas, 
June 25, 1906 

Obs. precip 

Increment 

Max. precip 

Thomasville, Ga., 
June 27, 1909 

Obs. precip 

Increment 

Max. precip 

Toledo, Ohio, 
June 24, 1911 

Obs. precip 

Increment 

Max. precip 



Time in minutes 



5 10 15 20 25 30 35 40 45 50 60 



0.12 
0.12 
0.34 

2.81 
0.32 

2.87 

4.30 
0.18 
4.30 

6.20 
0.14 
6 20 



0.38 
0.38 
42 



0.12 
0.12 
0.59 



0.45 
0.45 
0.90 



0.26 
0.26 
0.44 



21 

21 
71 



0.37 
0.37 
42 



0.30 
0.18 
65 

2.99 
0.18 
2.99 

4.52 
0.22 
4.52 

6.28 
0.08 
6.28 



0.42 0.72 
0.120.30 
0.98 1.25 

3.15 
0.07 
3.15 



0.80 
0.42 
0.82 



0.17 
0.05 




1.35 
0.90 
1.80 



0.70 
0.44 
0.86 



0.52 
0.31 
1.26 



79 
0.42 

1.79 



4.68 
0.16 
4.68 

6.32 
0.04 
6.32 



1 20 
0.40 
1.20 



0.45 
0.28 
1.40 



5.00 
0.32 
5.00 

6.36 
0.04 
6.36 



1.43 
0.23 
1.43 



0.62 
0.17 
1 



2.25 2.75 2.83 
0.90 0.50 0.08 
2.30 2.75 2.83 



1.12 
0.42 
1.16 



0.64 
(l 12 
1.83 



0.88 
0.09 
1 00 



0.97 
0.25 
1 .53 

3.25 
0.10 
3.25 

5.31 
0.31 
5.31 

6.43 
0.07 
6.43 



1.73 
0.30 
1.73 



0.90 
0.28 
2.10 



1.31 
0.34 
1 84 

3.35 
0.10 
3.25 

5.48 
0.17 

5.48 

6.49 
0.06 
6.49 



1.62 
0.31 
2.09 

3.50 
0.15 
3.50 

5.55 
0.07 
5.55 



1.42 
0.30 
1.42 



0.78 
0.14 

2.27 



1.27 
0.39 
1.27 



2 10 
0.37 
2.10 



d.32 
0.42 
2.38 



2 

0.06 

2 



1 65 
0.23 
1.65 



1.11 
0.33 
2.66 



1.62 
0.35 
1.62 



95 
0.33 
2.39 

3.75 
0.25 
3.75 

5.67 
0.12 
5.67 



22 
0.27 
2.57 

92 
17 
3.92 

5.90 
0.23 



2.31 2.42 
0.21J0.11 
2.31 2.42 



1.71 
0.39 
2.55 



1.87 2.19 
0.22 0.32 
1.872.19 



1.68 
0.57 
2.99 



1.88 
0.26 
1.88 



2.30 
0.59 
2 



2.55 
36 
2.55 



2.23 2 

0.550.71 

3.173.36 



2 00 
0.12 
2.00 



2.04 
04 
2.04 



2.49 
0.27 
2.69 

4.12 
0.20 
4.12 

06 
0.16 
6.06 



2.56 
0.14 
2.56 



2.57 
0.27 

2.88 



0.14 
2.70 



3.00 
0.43 
3.00 



2 
0.34 



3.38 
0.44 
3.56 



2.13 
0.09 
3.13 



2.75 
0.05 
2.75 



3.13 
0.13 
3.13 



3.15 
0.26 
3.15 



3.77 
0.39 
3.77 



3.40 
0.25 
3.40 



4.14 
0.37 
4.14 



3.37 
0.24 
3.37 



3.80 
0.40 



3.49 
0.12 
3.49 



4.03 
0.23 



3.80 4.03 



4.26 
0.12 
4.26 



172 



ELEMENTS OF HYDROLOGY 



TABLE 12. — DATA FOR 100 TYPICAL INTENSE RAIN- 
STORMS — 1896-1914 — (Concluded) 



No. 


Station 


93 


Topeka, Kan., 
Sept. 6, 1909 

Obs. precip 

Increment 


94 


Valentine, Neb., 
Aug. 12, 1909 




Increment 


95 


Washington, D. C, 
Aug. 10, 1897 




Increment 


96 


Washington, D. C, 
July 5, 1905 










97 


Washington, D. C, 
July 30, 1913 










98 


Wichita, Kan., 
Sept. 17, 1905 










99 


Wytheville, Va., 
July 21, 1908 










100 


Yankton, .S. D., 
May 26, 1912 















Time in minutes 



5 10 15 20 25 30 35 40 45 50 60 80 100 120 



0.09 
0.09 
0.27 



0.17 
0.17 
0.44 



0.18 
0.18 
0.54 



30 
30 
0.32 



0.52 
0.52 




0.23 
0.23 
0.50 



0.24 
0.24 
0.49 



0.22 
0.22 
0.50 



0.36 
0.27 
0.53 



0.34 
0.17 

0.83 



0.56 
0.38 
1.06 



0.54 
0.24 
0.63 



I 21 

II 69 

1 21 



0.36 
0.13 
91 



0.68 
0.44 
0.93 



0.72 
0.50 
0.90 



62 
0.26 
64 



0.47 
0.13 
1.23 



1.08 
0.52 
1.44 



0.75 
0.21 
81 



1.51 
0.30 
1.51 



0.41 
0.05 
1.25 



1.17 
0.49 
1.35 



1.12 
0.40 
1.27 



0.73 
0.11 
0.83 



0.65 
0.18 
1.60 



1.62 
0.54 
1.68 



0.93 
0.18 




1.56 
0.05 
1.56 



0.82 
0.41 
1.43 



1.59 
0.42 
1 59 



1.49 
0.37 
1.49 



0.92 
0.19 
1.01 



0.79 
0.14 
1 85 



1.86 
0.24 
1.86 



1.11 
0.18 
1.20 



1.32 
0.50 
1.56 



1.79 
0.20 
1.79 



1.67 
0.18 
1.67 



1.10 
0.18 
1.27 



1.19 

40 
2.04 



1 87 
0.01 

1.87 



1.42 
0.31 
1.44 



1.36 
0.26 
1.39 



1.58 
0.39 
2.22 



1 ss 

111 

1.88 



1.74 
0.32 
1.74 



1.48 
0.12 
1.58 



02 

0.44 

36 



1.90 
0.02 
1.90 



1.83 
0.09 
1.83 



1.66 1.84 1.972.17 
0.34j0.18 0.13 0.20 
1.77 2.18 2.23 2.36 



2.10 
0.31 
2.10 



1.71 
0.04 
1.71 



2.22 
0.12 
2.22 



1.77 
0.06 
1.77 



1.67 
0.19 
1.76 



2.39 
0.37 
2.54 



1.92 
0.02 
1.92 



1 

0.16 

1 



2.32 
0.10 
2.32 



1.85 
0.18 
1.90 



2.64 
0.25 
2.67 



2.25 
0.26 
2.25 



2.59 
0.42 
2.59 



2.14 
0.29 
2.19 



3.01 
0.37 
3.01 



2.72 
0.47 
2.72 



2.71 
0.57 
2.74 



2.21 
0.20 
3.21 



:i 23 
0.51 
3.23 



3.20 
0.49 
3.20 






PRECIPITATION 



173 



TABLE 13. — MOST EXCEPTIONAL RATE OF PRECIPITATION 

DURING ONE HUNDRED INTENSE RAINSTORMS — 

1896-1914 





Station 


Date 


Precipitation 


No. 












Amount, 


Time, 








inches 


minutes 


1 


Augusta, Ga. 


June 18, 1911 


1.24 


5 


2 


St. Louis, Mo. 


March 4, 1897 


0.88 


5 


3 


Denver, Colo. 


July 14, 1912 


0.87 


5 


4 


Atlantic City, N. J. 


May 31, 1906 


0.83 


5 


5 


Kansas City, Mo. 


May 31, 1896 


0.80 


5 


6 


Buffalo, N. Y. 


March 20, 1897 


0.79 


5 


7 


Cleveland, Ohio 


Aug. 29, 1903 


0.78 


5 


8 


Memphis, Tenn. 


March 9, 1901 


0.78 


5 


9 


St. Louis, Mo. 


May 1, 1898 


0.74 


5 


10 


Jacksonville, Fla. 


Aug. 16, 1901 


0.72 


5 


11 


Asheville, N. C. 


June 12, 1914 


0.70 


5 


12 


Indianapolis, Ind. 


Sept. 30, 1902 


0.69 


5 


13 


Moorhead, Minn. 


Aug. 29, 1908 


0.68 


5 


14 


Dallas, Texas 


Sept. 22, 1914 


0.62 


5 


15 


Taylor, Texas 


April 29, 1905 


1.80 


10 


16 


Raleigh, N. C. 


July 14, 1914 


1.35 


10 


17 


Washington, D. C. 


July 30, 1913 


1.21 


10 


18 


Bentonville, Ark. 


April 23, 1908 


1.19 


10 


19 


Cleveland, Ohio 


Aug. 20, 1901 


1.09 


10 


20 


Dodge City, Kansas 


July 17, 1911 


1.02 


10 


21 


Duluth, Minn. 


Aug. 12, 1910 


0.98 


10 


22 


Pensacola, Fla. 


Oct. 20, 1909 


2.29 


15 


23 


Thomasville, Ga. 


June 27, 1909 


1.83 


15 


24 


Anniston, Ala. 


Sept. 5, 1906 


1.81 


15 


25 


New Orleans, La. 


Sept. 30, 1905 


1.68 


15 


26 


New York City, N. Y. 


July 10, 1905 


1.63 


15 


27 


Kansas City, Mo. 


Sept. 15, 1914 


1.57 


15 


28 


Escanaba, Mich. 


July 12, 1903 


1.52 


15 


29 


Lynchburg, Va. 


June 24, 1905 


1.42 


15 


30 


Davenport, Iowa 


July 14, 1910 


1.38 


15 


31 


Philadelphia, Pa. 


Aug. 6, 1905 


1.35 


15 


32 


Cairo, 111. 


July 30, 1913 


1.32 


15 


33 


Chattanooga, Tenn. 


Aug. 22, 1912 


1.26 


15 


34 


Knoxville, Tenn. 


Aug. 4, 1905 


1.24 


15 


35 


Baltimore, Md. 


Aug. 25, 1911 


2.03 


20 


36 


Washington, D. C. 


Aug. 10, 1897 


1.68 


20 


37 


Cincinnati, Ohio 


May 20, 1902 


2.13 


25 


38 


Concordia, Kansas 


Aug. 26, 1908 


1.99 


25 


39 


Yankton, S. D. 


May 26, 1912 


1.67 


25 


40 


Richmond, Va. 


Aug. 19, 1908 


2.60 


30 


41 


Wytheville, Va. 


July 21, 1908 


2.10 


30 


42 


St. Paul, Minn. 


Aug. 9, 1902 


2.06 


30 


43 


Toledo, Ohio 


June 24, 1911 


1.88 


30 


44 


Birmingham, Ala. 


July 24, 1910 


1.87 


. 30 


45 


Lincoln, Neb. 


July 25, 1914 


2.78 


35 


46 


Concord, N. H. 


July 7, 1907 


2.60 


35 


47 


Minneapolis, Minn. 


Aug. 22, 1914 


2.15 


35 


48 


Chatanooga, Tenn. 


Aug. 17, 1912 


2.10 


35 


49 


Green Bay, Wis. 


Aug. 9, 1906 


2.03 


35 


50 


Grand Rapids, Mich. 


June 26, 1909 


1.86 


35 



174 



ELEMENTS OF HYDROLOGY 



TABLE 13. — MOST EXCEPTIONAL RATE OF PRECIPITATION 
DURING ONE HUNDRED INTENSE RAINSTORMS — 

1896-1914— (Concluded) 





Station 


Date 


Precipitation 


No. 












Amount, 


Time, 








inches 


minutes 


51 


Atlanta, Ga. 


Aug. 20, 1914 


2.89 


40 


52 


Tampa, P'la. 


June 20, 1905 


2.83 


40 


53 


Bismarck, N. D. 


Aug.. 9, 1909 


2.80 


40 


54 


Jacksonville, Fla. 


Sept. 6, 1907 


2.73 


40 


55 


Elkins, W. Va. 


Aug. 4, 1911 


2.22 


40 


56 


Sandusky, Ohio 


Aug. 7, 1906 


2.11 


40 


57 


Asheville, N. C. 


Aug. 12, 1911 


2.65 


45 


58 


Indianapolis, Ind. 


Aug. 13, 1913 


2.41 


45 


59 


Evansville, Ind. 


Aug. 10, 1908 


2.33 


45 


60 


Jupiter, Fla. 


Oct. 28, 1908 


3.66 


50 


61 


Lincoln, Neb. 


May 27, 1914 


2.72 


50 


62 


Springfield, 111. 


July 6, 1912 


2.70 


50 


63 


Wichita, Kansas 


Sept. 17, 1905 


2.59 


50 


64 


Meridian, Miss. 


Aug. 13, 1906 


3.63 


60 


65 


Lynchburg, Va. 


Sept. 3, 1907 


3.49 


60 


66 


Abilene, Texas 


July 31, 1911 


3.46 


60 


67 


Montgomery, Ala. 


May 30, 1905 


3.46 


60 


68 


Cairo, 111. 


June 28, 1905 


3.15 


60 


69 


Valentine, Neb. 


Aug. 12, 1909 


3.01 


60 


70 


St. Louis, Mo. 


July 14, 1912 


2.95 


60 


71 


Columbia, Mo. 


June 29, 1909 


2.73 


60 


72 


Oklahoma, Okla. 


June 23, 1908 


2.65 


60 


73 


Kansas City, Mo. 


Aug. 23, 1906 


5.45 


80 


74 


Marquette, Mich. 


June 23, 1907 


3.54 


80 


75 


Washington, D. C. 


July 5, 1905 


3.23 


80 


76 


Anniston, Ala. 


April 22, 1909 


2.84 


80 


77 


Rochester, N. Y. 


July 11, 1897 


2.74 


80 


78 


Duluth, Minn. 


July 21, 1909 


2.51 


80 


79 


Galveston, Texas 


Oct. 22, 1913 


6.52 


100 


80 


Dodge City, Kansas 


Sept. 16, 1906 


4.85 


100 


81 


Madison, Wis. 


Aug. 8, 1906 


4.84 


100 


82 


Taylor, Texas 


June 25, 1906 


4.03 


100 


83 


Atlanta, Ga. 


March 15, 1912 


3.37 


100 


84 


Des Moines, Iowa 


July 15, 1907 


3.29 


100 


85 


Topeka, Kansas 


Sept. 6, 1909 


3.20 


100 


86 


Pensacola, Fla. 


Sept. 29, 1906 


6.10 


115 


87 


Lincoln, Neb. 


June 5, 1914 


3.35 


115 


88 


Galveston, Texas 


April 23, 1904 


7.58 


120 


89 


Galveston, Texas 


Oct. 6, 1910 


6.28 


120 


90 


New York City, N. Y. 


Oct. 1, 1913 


6.20 


120 


91 


Shreveport, La. 


July 23, 1905 


5.00 


120 


92 


Norfolk, Va. 


Aug. 14, 1898 


4.73 


120 


93 


Miami, Fla. 


Nov. 8, 1914 


4.59 


120 


94 


Abilene, Texas 


May 22, 1908 


4.42 


120 


95 


Atlanta, Ga. 


July 23, 1898 


4.32 


120 


96 


Fort Worth, Texas 


Sept. 21, 1900 


4.32 


120 


97 


Houghton, Mich. 


Sept, 7, 1913 


4.28 


120 


98 


Abilene, Texas 


Oct, 22, 1908 


3.94 


120 


99 


Hannibal, Mo. 


July 29, 1910 


3.87 


120 


100 


Del Rio, Texas 


July 2, 1914 


3.56 


120 



PRECIPITATION 



175 



TABLE 13. — MOST EXCEPTIONAL RATE OF PRECIPITATION 
DURING THIRTY-EIGHT EARLIER RAINSTORMS 





Station 


Date 


Precipitation 


No. 












Amount, 


Time, 








inches 


minutes 


1 


Desmos, Ohio 


Sept. 5, 1890 


2.00 


5 


2 


Ft. McPherson, Neb. 


May 27, 1868 


1.50 


5 


3 


Kirkwood, S. C. 


Sept. 14, 1890 


1.50 


10 


4 


Huron, S. D. 


July 26, 1885 


1.30 


10 


5 


Albany, N. Y. 


July 10, 1876 


1.22 


10 


6 


Alpena, Mich. 


Sept. 20, 1884 


1.05 


11 


7 


Galveston, Texas 


June 4, 1871 


3.95 


14 


8 


Embarrass, Wis. 


May 28, 1881 


2.30 


15 


9 


Sandusky, Ohio 


July 11, 1879 


2.25 


15 


10 


Amano, Va. 


July 31, 1878 


1.56 


15 


11 


Ft. Randall, S. D. 


May 28, 1873 


1.56 


15 


12 


Havre, Tenn. 


Sept. 10, 1889 


3.00 


20 


13 


Jupiter, Fla. 


Aug. 21, 1893 . 


2.12 


20 


14 


West Leavenworth, Kan. 


July 21, 1887 


1.90 


20 


15 


Fort Scott, Kan. 


Oct. 2, 1881 


1.80 


20 


16 


Sheldon, Minn. 


June 23, 1890 


2.07 


25 


17 


Biscayne, Fla. 


March 28, 1874 


4.10 


30 


18 


Logansport, Md. 


July 7, 1879 


3.50 


30 


19 


Colorado Springs, Colo. 


Aug. 14, 1890 


2.75 


30 


20 


College Hill, Ohio 


May 27, 1888 


2.38 


30 


21 


Providence, R. I. 


Aug. 6, 1878 


3.50 


35 


22 


Newton, Penn. 


Aug. 5, 1843 


5.50 


40 


23 


Jacksonville, Fla. 


July 6, 1886 


3.49 


40 


24 


Black Rock, Ark. 


April 20, 1892 


3.42 


40 


25 


East Peoria, 111. 


June 13, 1893 


2.65 


40 


26 


Monroe, La. 


Sept. 22, 1890 


4.12 


45 


27 


Dodge City, Kan. 


June 19, 1888 


3.24 


45 


28 


Alexandria, S. D. 


May 21, 1893 


3.15 


45 


29 


Jupiter, Fla. 


Nov. 4, 1893 


3.50 


51 


30 


Tridelphia, W. Va. 


July 19, 1888 


6.90 


55 


31 


St. Louis, Mo. 


Aug. 15, 1848 


5.05 


60 


32 


Cumberland, Md. 


June 4, 1892 


4.64 


60 


33 


Atwood, 111. 


June 12, 1890 


4.36 


60 


34 


Galveston, Texas 


Feb. 22, 1888 


3.31 


60 


35 


Spooner, Wis. 


June 23, 1894 


3.00 


60 


36 


Rock Island, 111. 


July 13, 1889 


5.16 


75 


37 


Plover, Wis. 


Aug. 3, 1890 


4.50 


90 


38 


Brandywine, Pa. 


Aug. 5, 1843 


10.00 


120 



176 



ELEMENTS OF HYDROLOGY 



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PRECIPITATION 



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186 



ELEMENTS OF HYDROLOGY 







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PRECIPITATION 



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CHAPTER V 
EVAPORATION FROM WATER SURFACES 

The Water Cycle. — A quantity of water just equal to the 
precipitation which falls upon the land and water areas of the 
earth's surface in the course of several years must be evaporated 
again, otherwise there would have to be a progressive change in 
the vapor content of the air or an escape of water vapor from the 
upper atmosphere into space. Even our limited meteorological 
observations and our knowledge of gases, however, indicate that 
neither of these possibilities is a fact. As the variable amount 
of moisture in the earth's atmosphere represents but a fraction 
of an inch of precipitation, it follows that for the earth as a whole, 
precipitation and evaporation are two stages in a cycle of phe- 
nomena that has neither beginning nor end, but which may 
possibly be experiencing a small progressive increase or decrease. 

If the mean annual surface temperature of the earth is assumed 
to be constant, those factors which tend to increase evaporation 
from the land area will also tend to increase precipitation. 

Under the conditions of constant temperature, humidity and 
wind, evaporation from the large water surfaces of the earth 
must remain constant. 

A temporary increase in temperature results in increased 
evaporation and also increased precipitation. This is well shown 
in Fig. 48, p. 73, which gives the effect of changes in temperature 
in eastern United States on precipitation in Europe. 

If changes occur in the cultural conditions of the large land 
areas which increase evaporation, the result must inevitably be 
an increase in precipitation. On the other hand, if there are 
changes on the land areas which increase the amount of water 

which runs off over the earth's surface, or through the rock strata, 

188 



EVAPORATION FROM WATER SURFACES 189 

into the ocean, evaporation and consequently precipitation, must 
be reduced. 

So long as there is any runoff from the land areas, evaporation 
from the water areas of the earth's surface must exceed precipi- 
tation upon those areas, and, on the other hand, evaporation 
from the land areas must be less than the precipitation upon those 
areas. It follows, then, that the runoff from the land area repre- 
sents the excess of evaporation from the water area over pre- 
cipitation upon that area. As by far the greater portion of the 
water evaporated from the land area is re-precipitated upon that 
area, and as precipitation and evaporation over the water area 
remain substantially constant, the total runoff from the land 
area into the ocean must also remain substantially constant, 
irrespective of changes upon the land area which increase or de- 
crease evaporation from that area. The distribution of the total 
runoff will, of course, be changed. In the region of prevailing 
westerlies watersheds lying on the easterly side of the continents 
will be principally affected by such changes in evaporation and 
precipitation. 

Low- and high-pressure areas pass across the United States 
with average intervals of about 1000 miles in distance between 
them. As about 50 per cent of the evaporation from land occurs 
within three days after precipitation, most of the excess evapora- 
tion (assuming changes have occurred on the land area which 
have increased evaporation) will occur under the succeeding 
high and the moisture so evaporated will blow in toward the pre- 
ceding low and be re-precipitated. Evidently a portion of any 
such possible increased evaporation over the eastern 500 miles, 
say, of the United States, would result in increased precipitation 
over the Atlantic Ocean. This, in turn, would slightly decrease 
evaporation from the ocean and to this extent, only, reduce 
runoff from the land area. 

In view of these considerations, the difficulties attendant 
upon all efforts to find the effects of deforestation and culti- 
vation and similar changes upon any given watershed, reflected 



190 ELEMENTS OF HYDROLOGY 

in the flow of streams draining such watersheds, can be better 
appreciated. 

Of the precipitation which falls upon the land areas, a portion 
is evaporated; another portion is transpired by plants or used 
to form vegetable tissue; and still another portion of the pre- 
cipitation runs off from the surface of the land area through 
water courses or finds its way back to the sea through the earth 
and rock strata. 

Evaporation Defined. — Evaporation is the process by which 
water is changed from the liquid or the solid into the gaseous 
state. As temperature is but a measure of the average rate of 
motion of the molecules of any substance, it follows that some 
molecules are always moving at a much higher velocity than the 
average. Some of these extra-rapidly moving molecules are 
" bombarded " out through the surface film of water, into the 
atmosphere, so far beyond the influence of the force of cohesion 
that they do not return to the liquid, but remain in the space 
above as vapor. When the vapor over the water surface is rel- 
atively dense, some of the vapor molecules are caught in the 
water and join the liquid again. When the interchange of 
molecules is equal, evaporation is zero. This occurs when the 
dew-point temperature of the vapor above the water is just equal 
to the temperature of the liquid. While the dew-point tempera- 
ture of the vapor is lower than the temperature of the water, 
evaporation continues, but when it is higher, condensation occurs. 
For any given temperature, the fewer the number of molecules 
of vapor in a unit volume of space above the water surface, the 
more rapid the rate at which the upward moving molecules are 
lost from the liquid. 

Inasmuch as the process of evaporation consists of the ab- 
straction of the more rapidly moving molecules from the liquid 
mass, it follows that the average rate of motion of the remaining 
molecules must be reduced and, consequently, the temperature 
of the liquid lowered. In other words, evaporation " is a process 
of cooling." 



EVAPORATION FROM WATER SURFACES 191 

Effect of Temperature. — In discussing the subject of vapor 
pressure, it was pointed out that the pressure of saturated vapor 
doubles for every increase of from 15° to 20° F. in temperature. 
For the ordinary annual range of temperature, then, the pressure 
of saturated vapor will vary several hundred per cent. 

It was first pointed out by Dalton, over a century ago, that 
the rate of evaporation from a water surface, other conditions 
remaining constant, varies nearly as the difference between the 
maximum vapor pressure corresponding to the temperature of 
the water and the actual pressure of vapor present in the at- 
mosphere above the water. Vapor diffuses itself through the 
atmosphere somewhat slowly on account of the presence of the 
molecules of the dry gases. The principal means for the removal 
of the vapor which forms over all moist surfaces, is the bodily 
motion of the atmosphere. Since the air movement within a few 
feet of the land and water surface is very much slower than at 
higher elevations, there is always a considerable variation in the 
water vapor content of the lower few feet of the atmosphere. 
This variation consists not only of a variation in the relative 
humidity but in the actual amount of vapor present, as repre- 
sented by the vapor pressure. 

If we accept the principle enunciated by Dalton, that evapora- 
tion is governed by the difference between the vapor pressure 
corresponding to the water temperature and the actual pressure 
of the vapor present in the air above, and if the rate of reduction 
in the vapor content of the air from the earth's surface upward is 
uniform, it follows that the vapor pressure measured at almost 
any elevation above the earth's surface, when subtracted from 
the vapor pressure corresponding to the water temperature, will 
give a measure of evaporation. This is substantiated by the 
observations of Bigelow.* 

Inasmuch as the maximum vapor pressure is a function of the 
temperature, the actual pressure of the vapor present in the 

* Bigelow, Frank H., A Manual for Observers in Climatology and Evapo- 
ration: U. S. Weather Bureau, 1909, p. 33. 



192 ELEMENTS OF HYDROLOGY 

atmosphere must also be a function of the temperature, if the 
relative humidity remains constant. In other words, the rate of 
evaporation, according to Dalton's law, is approximately doubled 
for each 18 degrees rise in temperature, for constant humidity 
and wind velocity. Within the range of variation in monthly 
mean temperature occurring throughout most of the United 
States, the monthly mean rate of evaporation of free moisture 
will vary about 700 to 1200 per cent due to temperature changes 
alone. 

Effect of Barometric Pressure. — Several of the early writers 
concluded that evaporation varied inversely as the barometric 
pressure. The same allowance was made by Russell in his evapo- 
ration formula first published in the Monthly Weather Review 
in 1888. 

Stefan, in 1873, represented the effect of barometric pressure 

by the following expression: log (p - ^ — ) where P = baromet- 
ric pressure and p = maximum vapor pressure at the given 
temperature. (The value of this expression becomes infinity 
at the boiling point.) 

Fig. 140 shows the effect of barometric pressure on evaporation 
according to the formulas of Stefan and Russell. The two formu- 
las give almost identical results for all temperatures. 

Bigelow,* in his evaporation formula, completely neglects the 
effect of barometric pressure on evaporation, but in the discus- 
sion of his formula he does not state the reason why. 

Note: It is evident that widely divergent views respecting the effect of 
barometric pressure on evaporation are held by different investigators. It 
appears to the author that even though water boils freely at temperatures le:" 
than 212° F. under less than sea-level barometric pressure, it does not neces- 
sarily follow that reduction in barometric pressure, per se, increases evapora- 
tion. To say that, under any given pressure, water boils at a given tempera- 
ture, is merely another way of saying that the total pressure of the atmosphere, 
i.e., the combined pressure of the nitrogen, oxygen, C0 2 , water vapor, etc., are 
exactly equal to the maximum vapor pressure of the water at the temperature 
of the boiling point under those conditions. If the latent heat of vaporization 

* Bigelow, Frank H., Atmospheric Circulation and Radiation, p. 346. 



EVAPORATION FROM WATER SURFACES 



193 



of water were zero, it would instantaneously pass from the liquid to the gaseous 
state when the boiling temperature was reached. 

The various gases of the atmosphere exist independently of each other, 
except in so far as they retard the diffusion of other gases. Neither exerts a 
pressure on the other. While the distribution of oxygen and nitrogen in the 
atmosphere are governed, primarily, by the laws of Boyle and Charles, the 
distribution of water vapor is governed, primarily, by temperature. If, as 
150 r 



145 



MO 



135 



ft. 130 



i 125 



£120 



115 



110 



1(15 



100 

30 29 28 27 20 25 24 23 22 21 20 

Barometric Pressure - Inches Mercuiy 
Fig. 140. 

stated by Prof. Thomas Tate, vapor can diffuse itself through the other gases 
of the atmosphere more rapidly than it is formed from the surface of the water, 
it stands to reason that the total weight of the other gases above the water 
surface can have no material bearing upon the rate of evaporation, even though 
it has an effect upon the rate of diffusion and, particularly, upon the tempera- 
ture at which water passes freely from the liquid to the gaseous state. 

The author has in hand some experimental studies on the rate of evapora- 
tion from water in enclosed vessels in both quiet and circulating air, simulating, 
so far as possible, open air conditions. While these studies are incomplete, 
yet, they indicate only a small increase in the rate of evaporation even for one- 
third reduction in barometric pressure. 





















/ 








EFFECT OF 

BAROMETRIC PRESSURE 

ON 

EVAPORATION 




/ 


















































































































Graphs for 

Stefan Formula - Log ( -5 — - ) 

and 

Russell Formula - (-^-) 

are 
Practically Coincident 





































194 ELEMENTS OF HYDROLOGY 

It would seem that if vapor can diffuse through the ordinary calm at- 
mosphere more rapidly than it can form at the water surface, under ordinary 
open air temperatures, and if, moreover, vapor is usually carried away bodily 
by air currents still more rapidly than it can diffuse through the air, a reduction 
in barometric pressure — which is simply the removal of some of the molecules 
of nitrogen and oxygen which are in the path of the upward moving water 
vapor molecules — at best can only result in reducing the number of molecules 
of water vapor per cubic foot of space above the water. In other words, it can 
only result in a reduction of the actual vapor pressure above the water. Since 
the Dalton formula for evaporation, which the author has accepted, assumes 
evaporation to vary as the difference between the maximum vapor pressure 
at the water temperature and the actual vapor pressure in the air above the 
water, any effect of barometric pressure will have been taken into considera- 
tion, when the actual vapor pressure above the water surface has been deter- 
mined. 

The water vapor in the atmosphere is almost continually in a state of un- 
stable equilibrium. The vapor pressure at the earth's surface is usually at 
least 5 to 10 times the weight of the column of vapor above; hence, the water 
vapor at the surfaee can be held in equilibrium only by the obstruction pre- 
sented by the molecules of nitrogen and oxygen. 

As the vapor moves upward, or is carried up by air currents, it cools and 
precipitates; consequently, there is a continual flow of water vapor to higher 
altitudes. A reduction in barometric pressure would facilitate this flow of 
vapor, and h( ace would tend to lower the relative humidity at the water sur- 
face, but would not affect evaporation in any direct way. If the flow of 
vapor upward is entirely dependent upon the bodily motion of the air, a re- 
duction in barometric pressure could not affect evaporation, even in this 
indirect way. 

The author desires to reiterate that these conclusions are based upon un- 
completed laboratory studies and library researches, and must not be con- 
sidered final from his viewpoint. 

Effect of Relative Humidity. — Relative humidity affects 
evaporation only in so far as, when taken in connection with 
temperature, it is a measure of the amount of vapor present in 
the atmosphere. If the temperature of the water is higher than 
the temperature of the air, evaporation will continue even though 
the relative humidity a few feet above the water surface is 100 
per cent. 

For the condition of uniform and constant air and water tem- 
perature, evaporation is proportional to the saturation deficit. 
It is equal to a constant times the maximum vapor pressure cor- 
responding to the temperature, times one minus the relative 
humidity. 



EVAPORATION FROM WATER SURFACES 195 

Figs. 28 and 29, pp. 52 and 53, show graphically the variation 
in monthly mean relative humidity at a number of stations dis- 
tributed through the United States outside of the arid region of 
the West. It will be noted from these figures, that the monthly 
values of relative humidity in the several states vary by only 
about 15 to 20 per cent during the open season. Other condi- 
tions remaining constant, monthly mean evaporation, as the 
result of changes in monthly mean relative humidity, would vary 
only from 30 to 50 per cent. 

Effect of Wind Velocity. — The effect of air movement on 
evaporation has been given widely different weights by different 
writers. Weilenmann, Stelling, and Tate hold that evaporation 
varies, approximately, directly as the wind velocity. DeHeen, 
Shierbeck and Svenson hold that it varies as the square root of 
the wind velocity. Russell found a wind effect which, for wind 
velocities up to 15 or 20 miles per hour, can be approximately 

represented by the expression (l + jL where w represents 

wind velocity in miles per hour. 

FitzGerald * found that the wind effect could be represented 

w 
by the coefficient 1 + ~ • 

Bigelow, f in his first evaporation formula, used a wind fac- 
tor of about f 1 -f- qc ) " 

In his last published results, | Bigelow changed the wind factor 
to about ( 1 + 



The allowance to be made for change in wind velocity neces- 
sarily depends largely upon the elevation of the anemometer 
with reference to the surface from which evaporation is being 
measured. In so far as the author has had access to the original 

* FitzGerald, Desmond, Trans. Am. Soc. C. E., XV, p. 581. 

t Bigelow, Frank H., A Manual for Observers in Climatology and Evapora- 
tion, p. 28. 

X Atmospheric Circulation and Radiation, p. 346, and Bulletin No. 2, 
Argentine Meteorological Office, p. 39. 



196 ELEMENTS OF HYDROLOGY 

published results, it would appear that the wind effects above 
referred to had been based upon a wind velocity observed at 
the elevation of the water surface in the basin from which 
evaporation was measured. The practicing engineer, however, 
is usually limited to wind velocity as observed by the U. S. 
Weather Bureau, which, in general, represents a velocity from 
two to three times that at the surface of the ground. 

The effect of wind velocity on the evaporation of moisture 
from a broad expanse would appear to be primarily its effect 
in removing the vapor which forms more rapidly over the water 
surface than it can diffuse through the atmosphere above. If 
the rate of evaporation is determined by the vapor pressure 
gradient between the water surface and the upper atmosphere, 
it is not all clear why, when the actual pressure of vapor present 
in the air a short distance above the water has been determined, 
the effect of wind velocity has not already been taken account of. 
The effect of wind is to lower the relative humidity at the point 
of observation, if this is within a few feet of the water surface. 
Where a small surface of water is exposed to evaporation in 
quiescent air, a blanket of vapor soon forms above the water, 
which greatly reduces evaporation. If, under these conditions, 
however, a measurement of relative humidity is made rather 
close to the water surface, it will be found that the space is 
occupied by nearly saturated vapor. If the air is next set in 
motion, there will be a decided increase in the rate of evapora- 
tion which will also be indicated, however, by a great drop in 
relative humidity. Observations of relative humidity made at 
some distance from the water surface would not reflect the wind 
effect; consequently, it would appear correct to make an allow- 
ance for wind effect on the evaporation of moisture from small 
or non-uniformly moist surfaces when relative humidity is ob- 
served in a standard Weather Bureau shelter nearby, but to 
make no allowance for wind effect when the observations for 
relative humidity are made above a large water surface. 

After checking observed and computed evaporation from pans 



EVAPORATION FROM WATER SURFACES 



197 



at a number of stations, using various wind factors, the author 

has tentatively adopted ( 1 + ^J as representing the effect 

of wind on the evaporation of free moisture from the surface 
of very small bodies of water, where w represents wind 
velocity in miles per hour, as observed by the United States 

Weather Bureau. Using a wind factor of (l + TTj) the vari- 
ation in evaporation due to change in monthly mean wind 
velocity as shown graphically in Fig. 22, page 37, for a number 
of states, amounts to only about 20 to 30 per cent. 

10 





























































































































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Feb. Mar. April May June July Aug. Sept. Oct. .Nov. Dec. 

Fig. 141. — Monthly Mean Climatological Data, St. Paul, Minn. 

Relative Effects. — Fig. 141 shows the monthly mean rela- 
tive humidity, wind velocity, air temperature, maximum vapor 
pressure and actual vapor pressure in the atmosphere at 
St. Paul, Minn. Neither relative humidity nor wind velocity, 



198 ELEMENTS OF HYDROLOGY 

it will be observed, varies between wide limits. The difference 
between the maximum and actual vapor pressure, however, i.e., 
the variation in the factor which virtually determines evapora- 
tion, shows a variation of several hundred per cent. 

Evaporation Formulas. — The literature bearing on the 
subject of evaporation is very extensive. The most complete 
bibliography published to date is that prepared for the Monthly 
Weather Review of 1908 and 1909 by Mrs. Grace Livingston. 
It covers 849 references between the dates of 1670 and 1909. 

A large number of evaporation formulas have been proposed, 
but aside from the Dalton law already mentioned, specific 
reference will be made here to only two formulas, namely Bige- 
low's and Russell's. A full discussion of the data and consider- 
ations underlying Bigelow's formula is given in Bulletin No. 
2 of the Argentine Meteorological Office published in 1912. 
Bigelow's formula for evaporation from a large water surface is: 

E = 0.023 -^|(1 + 0.07 w), 
ed db 

where E = the evaporation in centimeters during four hours 
time ; 

e d = the vapor pressure in millimeters at the dew- 
point temperature of the air; 

c„ = the vapor pressure at the water temperature; 

w = the wind velocity at the surface of the water in 
kilometers per hour; 

de 

-To = the rate of change in the maximum vapor 

pressure with temperature. 

Russell's evaporation formula, fully discussed by him in the 

Monthly Weather Review of •September, 1888, is: 

30 ( ) 

E = y j Ap w + B{y w - p d ) > , 

E — evaporation in inches per month; 
p w = vapor tension, in inches of mercury, correspond- 
ing to monthly mean wet-bulb temperature; 



EVAPORATION FROM WATER SURFACES 



199 



p d = vapor tension, in inches of mercury, correspond- 
ing to monthly mean dew-point temperature; 
b — mean barometric pressure, in inches of mercury; 
A = 1.96; 
B = 43.88. 

The values for A and B were derived by the method of 
least squares, from the Piche evaporometer observations for 
June, 1888, at the 18 stations listed in Table 17. 



TABLE 17. — RUSSELL'S PICHE EVAPOROMETER 
OBSERVATIONS 



Station 



Boston 

New York. . . 
Washington. 
Cincinnati. . . 
Memphis. . . . 
New Orleans 

Chicago 

St. Louis. . . . 

Keeler 

Yuma 

El Paso 

Dodge City. . 

San Antonio. 

Omaha 

Denver 

St. Vincent. . 

Helena 

Boise City. . . 



Tempera- 


Evapora- 




Wind veloc- 


ture in de- 
grees 


tion in 
inches 


humidity, 


ity in 
miles per 


Fahrenheit 


depth 




hour 


66.8 


5.16 


65.0 


10.2 


71.4 


4.49 


67.6 


8.3 


73.0 


4.64 


68.0 


4.8 


74.2 


6.22 


56.6 


6.1 


75.4 


4.33 


70.8 


4.8 


77.3 


3.82 


77.7 


6.8 


67.4 


5.59 


64.1 


10.3 


73.2 


6.18 


68.5 


9.7 


73.9 


11.66 


23.0 


7.9 


85.6 


13.87 


25.3 


7.3 


83.0 


13.91 


24.1 


8.2 


74.5 


7.80 


53.0 


11.6 


78.0 


2.76 


75.3 


8.1 


70.0 


7.01 


63.2 


7.6 


68.4 


9.42 


31.4 


8.0 


62.8 


5.63 


69.5 


7.6 


58.8 


4.88 


56.6 


7.9 


64.2 


5.83 


48.8 


3.1 



Barometer 
in inches 
mercury 



29.8 
29.7 
29.8 
29.3 
29.6 
29.9 

29.2 
29.3 
26.2 
29.6 
26.1 
27.3 

29.1 

28.7 
24.7 
28.9 
25.7 
27.0 



With this formula and the means of tri-daily determinations 
of dew-point and wet-bulb temperatures in standard Weather 
Bureau shelters during 1887 and 1888 as a basis, Russell prepared 
his well-known evaporation tables for Signal Service Stations 
in the United States. These tables have been reprinted in 
several books — not always, however, accompanied by a state- 
ment of what the tables really represent. 

In deriving his formula, Russell first reduced the evaporation 
observed with the Piche evaporometer by one quarter, on the 



200 ELEMENTS OF HYDROLOGY 

basis of measurements of evaporation from dishes of water 
placed in the Weather Bureau shelters. He also neglected the 
effect of wind velocity because by doing so his formula better 
fitted the observational data. There was considerable variation 
in the observed wind velocity at the several stations during 
June, 1888, as shown by Table 17. Moreover, Russell found 
that at a wind velocity of five miles per hour, the evaporation 
from a Piche was 2.2 times that from one in quiet air; at 
ten miles 3.8 times; and at a wind velocity of 15 miles per hour, 
it was 4.9 times that in quiet air. The wind velocity measured 
with an anemometer set up inside of a standard shelter at 
Washington, D. C, for eight days, gave a value of 3.48 miles an 
hour, which was only 52 per cent of the velocity outside. 

In deriving his formula, Russell also increased the observed 
evaporation in proportion to the relation of 30 to the observed 
barometric pressure, that is, the observed evaporation at Denver, 
for example, where the barometer read 24.7 inches was multiplied 

by 7^7 or 1-21 before determining the constants of the equation. 

In comparing evaporation from a Piche with evaporation 
from a reservoir, it is necessary to take account of the fact 
stated by Russell in the Monthly Weather Review * that: 

"In the case of the Piche evaporometer the temper- 
ature of the evaporating water is strictly that of a wet- 
bulb thermometer exposed at the same place." 
The Piche evaporometer observations represent the evap- 
oration at an average wind velocity at the instrument of ap- 
proximately 3^ miles per hour. 

On the 1 other hand, as stated by Russell: 

.;•, , "The effect of the high exposure of the shelters is to 

make the figures too great, the wind action being far 

,. greater at the height of the shelters than at the level 

of the ground. The evaporation taking place from a 

small paper disk, as in the results obtained from the 

* September, 1888, p. 237. 



EVAPORATION FROM WATER SURFACES 201 

Piche instrument, has a tendency to be too small, 
as the determining temperature of evaporation is that 
of a wet-bulb thermometer exposed under similar cir- 
cumstances. In the case of a body of water the de- 
termining temperature of evaporation is nearly that 
of the average temperature of the air." 
Comparison of Evaporation Formulas. — Figs. 142 and 143 
show graphically the relative evaporation given by Bigelow's 
and Russell's formulas, and by the Dalton law, using the au- 
thor's wind factor. In order to permit a better comparison of 
the three formulas, Fig. 142 was drawn to show the relation 
between monthly evaporation and monthly mean temperature 
for constant relative humidities of 50 and 70 per cent and Fig. 
143 to show the relation between monthly evaporation and 
monthly mean relative humidity for constant temperatures 
of 50 and 77 degrees Fahrenheit. A constant wind velocity 
of 15 kilometers or 9.3 miles per hour was assumed for all con- 
ditions of temperature and humidity. Air and water temper- 
atures were assumed uniform except in the case of Russell's 
formula, which is based on wet-bulb thermometer temperatures 
for the water and which gives an evaporation loss equal to 
three-quarters of that from a Piche. 

These diagrams show outstanding differences between the 
three formulas. On the whole, Russell's formula gives smaller 
evaporation losses than the other two. As no allowance is 
made in his formula for wind effect, the values would have 
been relatively greater if a lower wind velocity had been 
used in the other two formulas. Bigelow's formula gives 
very high losses for relative humidities greater than 80 per 
cent and less than 25 per cent. An evaporation of nearly 
five inches per month at a temperature of 77 degrees, even 
though the relative humidity is 100 per cent, seems clearly 
impossible, unless air and water are not at the same temperature. 
Similarly, the nearly constant rate of evaporation, with great 
changes in relative humidity near 100 per cent and the rapidly 



202 



ELEMENTS OF HYDROLOGY 




Relative Humidity 70$. 
Relative Hud idity 50$' 



RELATION BETWEEN 

TEMPERATURE AND EVAPORATION 

ACCORDING TO 

VARIOUS FORMULAS. 



6 8 10 12 14 

Monthly Evaporation - Inches Depth 

Fig. 142. 



16 



18 



30 



10 



,20 



g50 



(50 



.2? 70 



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'.10 



100 















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RELATION BETWEEN 
RELATIVE HUMIDITY 
AND EVAPORATION 

ACCORDING TO 
VARIOUS FORMULAS 






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1 Is 

r / 


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6 8 10 12 14 16 

Monthly Evaporation— Inches Depth 

Fig. 143. 



EVAPORATION FROM WATER SURFACES 203 

increasing rate of evaporation at low relative humidities, ap- 
proaching infinity at zero, do not appear reasonable. When- 
ever the water temperature is higher than the air temperature, 
evaporation will not be zero even when the relative humidity is 
100 per cent and Bigelow's comments* relative to a continu- 
ation "sometimes to a surprising amount" of the evaporation 
loss from pans, in California and in Maine, during dense fogs, 
do not prove the Dalton law incorrect, by any means, as the 
air during a fog is invariably cooler than the water. 

In presenting observational data in support of his formula, 
Bigelow makes an effort to attribute the discrepancy between 
observed and computed evaporation loss to the expansion and 
contraction of the water in the evaporation pan.f 

It is true, of course, that when the temperature rises, the 
water expands, so that the observed elevation of the water 
surface during periods of rising temperature is greater, and, 
consequently, the observed evaporation loss less than the true 
loss and vice versa during periods of falling temperature. These 
discrepancies, however, are not at all comparable with most 
of the discrepancies shown in Bigelow's Table 5, representative 
samples of which are shown in Table 18. 

The data in Bigelow's Table 5, show 18 variations at 2 p.m. 
in the right direction and 22 in the wrong. Of the 10 p.m. 
data, there are 19 variations in the right direction and 21 in 
the wrong. 

It is apparent from Table 18 that the evaporation computed 
by means of Bigelow's formula frequently differs from the ob- 
served evaporation for four-hour periods by 15 to 20 per cent. 
After a careful study of Bigelow's work, the author has con- 

* Bulletin No. 2, Argentine Meteorological Office, p. 35. 

t Some observational data are presented by Bigelow on p. 32 of the Argen- 
tine Report in support of the above contention. A numerical quantity (given 
as +0.0046 but apparently +0.0029) resulting from averaging 10 plus values 
varying from 0.0000 to +0.0204 and 8 minus values varying from —0.0008 to 
—0.0141 is set forth as comparing favorably with a theoretically required 
value of +0.0048. Such divergent observational data can hardly be taken 
seriously in support of any contention whatsoever. 



204 



ELEMENTS OF HYDROLOGY 



eluded to retain, for the present at least, the old Dalton 
formula. Further discussion of Bigelow's formula will be found 
in the March and April, 1916, Proc. Am. Soc. C. E. 



TABLE 18. — RATIO OF OBSERVED TO COMPUTED 

FOUR-HOUR EVAPORATION AT TYPICAL STATIONS, TAKEN 

FROM BIGELOW'S TABLE NO. 5 * AND EXPRESSED 

IN PER CENT 



Station 


2 A.M. 


6 A.M. 


10 a.m. 


2 P.M. 


6 P.M. 


10 p.m. 


Birmingham, Alabama 


79 
80 

109 
100 


89 
89 

91 
95 


113 
114 

96 

72 


131 
124 

108 
105 


110 
101 

100 
126 


77 


Cincinnati, Ohio 

Salton Sea, California, Tower 1, 

Pan 4 

Avalon, N. M 


91 

95 
103 



Bulletin No. 2, Argentine Meteorological Office, p. 23. 



TABLE 19. — CORRECTION FOR SIZE OF EXPOSED 
EVAPORATION PANS 



Size of pan 


Relative evaporation 


Grunsky 


Bigelow 


2 foot, 


1.87 
1.56 
1.43 
1.30 
1.00 


1.82 

1.44 
1.24 
1.00 


3 " ... 


4 " 


6 " 


Large water surface 



Correction for Size of Pan. — There does not appear to 
be any good reason for making a substantial reduction in evap- 
oration from a large water surface as compared with evapora- 
tion from a pan floated in the same body of water, as proposed 
by Bigelow and others. Differences between evaporation from 
large bodies of water and from evaporation pans may be 
ascribed, mainly, to differences in temperature as the result 
of the use of too shallow pans and the heating effects of the 
portion of the pan projecting above the water surface. When 
deep, fully immersed pans are used, comparable results are 
obtained. For pans entirely exposed above land or water sur- 



EVAPORATION FROM WATER SURFACES 205 

faces, however, a correction should be made. Grunsky * has 
proposed a correction based mainly upon the relation between 
wetted perimeter and area of pan which agrees reasonably well 
with Bigelow's observations on exposed or partially immersed 
pans. 

Methods of Measurement. — Measurements of the evapora- 
tion from pans of water set in the ground or floated from rafts 
in large bodies of water have been made in a considerable 
number of places in the United States and elsewhere. Both 
square and round pans have been used, although the preferable 
piece of apparatus would appear to be a strong circular pan, 
3 feet in diameter and not less than 18 inches deep, with 
a sharp-pointed indicator in the center. A common mode of 
procedure, in measuring evaporation, is to add, each day, an 
amount of water equal to what evaporated during the pre- 
vious 24-hour period. The water is usually added by cup- 
fuls representing t <i<t inch in depth over the surface of the 
evaporating pan, until the water level is again up to the top 
of the sharp-pointed index in the center of the pan. A rain 
gage placed nearby is used as a measure of the precipitation 
on the evaporation pan for which correction must be made. 
The use of a circular pan has the advantage of always giving 
the correct height of water even though the pan may not be 
level. 

By far the best way of making an observational determi- 
nation of evaporation from a large water surface is to use the 
floating pan, even though it is often difficult to prevent the 
splash of water both in and out of the pan as the result of wave 
action. The use of pans suspended above the water or placed 
in the soil nearby, usually involves still greater possibilities 
for error. Fine brass wire netting, coiled into a spiral and 
placed in the evaporation pan but not permitted to project 
above the water surface, has been found to produce a very 

* Grunsky, C. E., Proceedings American Society Civil Engineers, April, 
1916, p. 562. 



206 



ELEMENTS OF HYDROLOGY 



satisfactory baffling effect. The evaporation pan should be 
bound with heavy straps of iron so as to prevent distortion, par- 
ticularly at the base where the index is fastened, and should 
preferably be not less than 3 feet in diameter and not less 
than 18 inches deep, the water being maintained as high in the 
dish as wave action permits. 

In determining the evaporating power of the atmosphere, 
botanists are making extensive use of porous-cup atmometers. 
One of the best types in use is that invented by B. E. Living- 
stone, and described by him in the December, 1907, "Plant 
World," p. 271. 

Observed Evaporation. — Tables 20 to 25 summarize some 
of the best records of actual observed evaporation from pans 
floated in relatively small bodies of water. These records 
all cover several years' observations. 



TABLE 20. — OBSERVED EVAPORATION 

AT UNIVERSITY, N. D., 

1905-1916, inclusive 



TABLE 21.— 

OBSERVED 

EVAPORATION 

AT GRAND 

RIVER LOCK, 

WIS., 1905-1913, 

inclusive 



Month 


Monthly mean air 
temperature, degrees F. 


Monthly mean evapora- 
tion, inches depth 


Monthly 
mean air 
tempera- 
ture, 
degrees F. 


Monthly 

mean 
evapora- 
tion, inches 
depth 




1905-13* 


1905-16 


1905-13* 


1905-16 






January 

February .... 

March 

April 

May 


45f 

52 

65 

67 

66 

57 

45 

34f 


45f 

52 

64 

68 

65 

57 

45 

36f 


3.37f 

4.03 

5.00 

5.81 

4.60 

3.57 

2.02 

0.52f 


3.31f 

4.09 

4.79 

5.69 

4.73 

3.66 

2.14 

0.86t 


45 
54 
64 
68 
65 
59 
48 
41t 


2.83 
4.35 


June 

July 


5.52 
5.74 


August 

September . . . 

October 

November. . . 


4.46 
3.45 
2.22 
1.09f 



* These values plotted in Fig. 144. 

t Observations extended over portions of the month only. 



EVAPORATION FROM WATER SURFACES 



207 



TABLE 22. — OBSERVED EVAPORATION 

AT BOSTON, MASSACHUSETTS, 

1875-1890 inclusive 



TABLE 23. — OB- 
SERVED EVAPORA- 
TION AT KINGS- 
BURG, CALIF., Nov., 
1881-1885 inclusive 



Month 


Monthly mean 

air tempera- 
ture,* degrees F. 


Monthly mean 

evaporation, inches 

depth 


Monthly mean 

air tempera- 
ture,* degrees F. 


Monthly mean 
evaporation, 
inches depth 






1875-1885 


1875-1890 






January 

February 

March 

April 

May 


27 ' 

28 

34 

44.5 

58 

67 

71 

69 

62 

52 

40 

30 


0.90t 

1.20f 

l.SOf 

3. 10t 

4.61 

5.86 

6.28 

5.49 

4.09 

2.95 

1.63 

1.20t 


0.96t 

1.05t 

1.70t 

2.97t 

4.46 

5.54 

5.98 

5.50 

4.12 

3.16 

2.25 

1.51 


45.3 
50.2 
54.4 
60.8 
67.4 
74.1 
82.1 
81.0 
73.8 
64.2 
54.6 
47.0 


0.77 
1.25 
2.46 
2.56 
3 39 


June 

July 

August 

September. . . . 

October 

November. . . . 
December .... 


5.80 
7.55 
8.65 
6.48 
4.05 
2.12 
1.19 



* Values taken from curve, 
t Values largely estimated. 

* Mean temperature 1888 to 1902 at Fresno in same valley 20 miles S. E. 



TABLE 24. — OBSERVED EVAPORATION 
NEAR INDEPENDENCE, CALIF., 

1908-1911 inclusive 



TABLE 25. — OB- 
SERVED EVAPORA- 
TION AT LEE BRIDGE, 
ENGLAND, 1860-1873 
inclusive 



Month 


Monthly mean 

air tempera- 
ture, degrees F. 


Monthly mean 
evaporation, 
inches depth 


Monthly mean 
air tempera- 
ture, degrees F. 


Monthly mean 
evaporation, 
inches depth 


January 

February 

March 


40.2 
39.8 
49.2 
56.5 
62.5 
73.2 
77.5 
76.5 
67.3 
56.6 
47.7 
39.0 


1.66 
2.42 
4.52 
6.87 
8.63 
10.00 
9.45 
8.10 
6.07 
3.87 
2.49 
1.37 


38.5 
40.8 
42.5 
48.1 
54.2 
60.2 
64.0 
63.3 
58.4 
50.6 
43.9 
39.5 


0.76 
0.60 
1.07 


April 


2.10 


May 

June 

July 


2.75 
3.14 
3.44 


August 

September 


2.85 
1.60 


October 


1.06 


November 


0.71 


December 


0.62 







The observations at University, N. D., were made by Prof. 
E. F. Chandler for the U. S. Geological Survey. Those at Grand 
River Lock, Wisconsin, were made by the U. S. Engineer De- 



208 ELEMENTS OF HYDROLOGY 

partment. Both the Grand River Lock and the University, 
N. D., evaporation stations are on small shallow bodies of water. 
The mean relative humidity at the North Dakota station is 
slightly less and the wind velocity slightly greater than at 
the Wisconsin station. 

The observations at Boston, Mass., were made by Desmond 
FitzGerald in the Chestnut Hill reservoir and are fully de- 
scribed by him in Trans. Am. Soc. C. E., Vol. XV, p. 581. 
Those at Mt. Hope, N. Y. were made by the City Engineer's 
Office of Rochester, New York. 

The observations at Kingsburg, Calif., were made by C. E. 
Grunsky under the direction of the State Engineer of Cali- 
fornia. Those at Lee Bridge near London, England, were made 
by Chas. Greaves and are described in Minutes of Proceed- 
ings, Inst. C. E., Vol. XLV, p. 19. 

In discussing the Kingsburg observations, Grunsky states 
that the values are probably somewhat small on account of 
protection which the pan derived from high banks and a fringe 
of low trees at a nearby bridge, and also that the temperature 
of the river water was probably less than that which would 
have prevailed in an open body of water. Comparison of the 
observations with other data also indicates that the evaporation 
is lower than would be expected for the given air temperatures, 
and that spring evaporation is less for the same temperature 
than fall evaporation. This is undoubtedly due to the fact that 
Kings River, on which the observations were taken, is a snow- 
fed stream. 

The observations near Independence, Calif., were made by 
Chas. H. Lee of the Department of Public Works, Los Angeles, 
in cooperation with the U. S. Geological Survey and the State 
of California. The full results are published in Water Supply 
Paper No. 294. 

The data presented in Tables 20 to 25 have been shown 
graphically in Figs. 144 to 148. The greater evaporation for 
the same air temperature during the spring than during the 



EVAPORATION FROM WATER SURFACES 



209 



fall results from the generally lower relative humidity and the 
higher wind velocity at a time when the temperature is rising. 
Apparently the capacity of the air for moisture is increased 
at a more rapid rate than evaporation from land and water 
areas can meet; consequently, the moisture content drops 
and the rate of evaporation increases. In the case of deep 
bodies of water the water temperature lags behind the air 
temperature and the spring evaporation, for the same air tem- 
perature, is less than the fall evaporation. 



Bd 
















































































































































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v- 










EVAPORATION FROM SHALLOW WATER 

o = Mean Observed Evaporation at University > T .D. 1905 to 1913 
• = Mean Observed Evap. at Grand River Lock, Wis.1905 to 1913 
■ — Mean Computed Evaporation at St. Paul Minn. 






o 
















« 






■ji 






















20 




<37 
















































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f/m 
















































































fl s 












































































10 




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2 3.4 5 6 

Monthly Evaporation, Inches Depth 

Fig. 144. 



The monthly mean rate of evaporation from shallow water 
at St. Paul, Minn., and Mount Hope, N. Y., computed by means 
of the Dalton Law, using the author's wind factor, together 
with the necessary observed meteorological phenomena, is given 
in Tables 2fi and 27. 



210 

80 


















ELEMENTS 




OF 


HYDROLOGY 














































! 
























































_L_ 






















































EVAPORATION FROM WATER 

OBSERVED BY FITZGERALD 

AT 

BOSTON, MASS. 
































































70 




















K 
























P 




it 




























o 




























> 








































¥ 
















fe 








































































w 

% 60 
u 








































4 


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bo 












































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4- 


























M 








































































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3 50 








































































ei 








































































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2 30 




















































































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Mean 1875 to 1885 • bserved o Estimated • 
Mean 1875 to 1890- a ■ 








S 








■S 








































































































































































































































































































































































































































































10 







































































2 3 4 5 

Montlily Evaporation - Inches Depth 

Fig. 145. 

























































































































































































































































































































































































Jul 


Eg 


























so 






















































































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a. 








































































































































































































































































































































































■J 


m 


K' 








"Sept 
































70 








































































































































































































































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a 


<•• 














































































































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I" 


















Opt 
























































60 






































































































































































































































































































































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ell. 
































































































.». 












































































50 










'e 


i. 
















































































































































EVAPORATION PROM WATER 

OBSERVED BY C.E. G.RUNSKY 

AT 

KINGSBURG.CAL. 

Nov. 1881 to Oct. 1885. 






























'\ 


























































J 


u 


.• 




































































































































40 


















































































































































































































| 
































































































































































































































?r> 





































































































3 15 6 7 

Monthly Evaporation -Inches Depth 



Fig. 146. 



EVAPORATION FROM WATER SURFACES 



211 

































































































^T* 
















































































t 












MulV 




































































































































































































Jum jf 


































































































































































































































































































































































































































































































.: 


lay 














































































































































































































































( 


>ct.. 
































































































































Api 
























































































































































































































































































\l 


ll 














































































N. 


V 






























































































































































































































































































, 




























































































1 


<■< 






ll 


n 






F 


eh. 


























EVAPORATION FROM WATER 

OBSERVED BY CHAS. H. LEE 

AT 

INDEPENDENCE, CAL. 

Sept. 1908 to Apr. 1911. 


















































































- 
























































































































































































































































































































































































1/ 




































































































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1 








1 










'. 










' 










I 




















t 




















E 










9 








lfl 



Monthly Evaporation - Inches Depth 

Fig. 147. 



















































































































































































































































;<> 


























































































































































































































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60° 








































































-S 


01 


t.- 
















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ie 






















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V 


• 


/Men. 












































40 








p'eL 




1 1 












































r 


01 








an# EVAPORATION FROM WATER 

OBSERVED BY CHARLES GREAVES 
AT 












f\ 
























30 












LEE BRIDGE, N 


tAK LUND 


UN, tNULANU. 


- 












1 








1 






1860-1873 










































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( 


i 










1 










> 










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i 


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i 








6 



Monthly Evaporation— Inches Depth 
Fig. 148. 



212 ELEMENTS OF HYDROLOGY 

TABLE 26. — COMPUTED EVAPORATION AT ST. PAUL, MINN. 





3 
O 

a. 

a 

H 


> a 

Is 


Relative 
humidity, 
per cent 


— 3 
a £ 

is a 


."£ o 
o u 
~S » 
> a 

3 7Z 


a 
o 

as 

!§• 

'o 


6 m 

> 8 


Month 


Mean 

Of 8 A.M. 

■and 

8P.M.f 


Mean 4 


S -2 

,9« 


January 


11.6 
15.0 

28.2 
45.7 
58.2 
67.4 
72.1 
69.5 
60.3 
48.1 
30.9 
19.3 


0.069 
0.081 
0.151 
0.306 
0.485 
0.670 
0.786 
0.720 
0.523 
0.335 
0.171 
0.099 


80 
79 
74 
65 
64 
68 
66 
69 
72 
72 
75 
79 


81 

79 
75 
66 
65 

67 

1167-5 
69 
72 
73 
76 
81 


0.013 
0.017 
0.038 
0.104 
0.170 
0.221 
0.255 
0.223 
0.146 
0.091 
0.041 
0.019 


7.8 
8.3 
8.8 
9.3 
8.7 
7.7 
7.1 
7.1 
8.0 
8.5 
8.1 
7.8 


0.90 
0.84 
1.60 
2.33 
3.12 
4.41 
3.40 
3.46 
3.42 
2.34 
1.30 
1.06 


35 


February 


47 


March 


1 07 


April 


3 02 


May 


4 76 


June 


5 88 


July 


6 55 


August 


5 72 


September 

October 


3.94 
2 53 


November 

December 


1.11 

0.51 


Annual 


43.9 




72 








28.68 















* Mean of 43 years, 1871 to 1913, inclusive. 
t Mean of 24 years, 1888 to 1911, inclusive. 
t As modified by Minneapolis records. 
§ Mean of 36 years, 1873 to 1908, inclusive. 
f. Mean of 43 years, 1871 to 1913, inclusive. 
IT As modified by Minneapolis, Moorhead, and LaCrosse records. 



TABLE 27. — COMPUTED AND OBSERVED EVAPORATION 
AT MT. HOPE, N. Y. 





Tempera- 
ture 


>> 

43 

-3 
S 

3 
-S 
93 
> 

<A 


Maximum 

vapor 

pressure 


U 

o t- 

S 1 a 

. > a 

> 3 
4> to 

o a 


Difference 
in vapor 
pressure 


>> 

'S 
o 
"3 
> 

a 


a 
o 

CO 

'o. 

a> 

Fh 


o, 

C3 
> 

» 3 
T3.2 

* « 

S 
o 
O 

1.21 
1.26 
1.63 

2.82 
3.88 
4.70 
5.40 
5.08 
4.08 
2.73 
1.80 
1.28 




Month 


a © 

•-T3 
p.* <s 

-~.fi 


a 
a* 


1^ 


s _■ 

° -3 

<5 o. 


a) 5 

.fa <S 
<J P. 


S p 

•8 3 


£ 2 

# o 
O > 


Jan 

Feb 

Mar 

Apr 

May... 
June 
July .... 
Aug. . . . 
Sept, . . . 

Oct 

Nov. . . . 
Dec 


24.8 
23.3 
34.1 
46.7 
60.1 
70.5 
74.7 
72.1 
65.7 
53.1 
39.9 
28.9 


32.5 
32.3 
35.8 
46.6 
59.0 
68.2 
72.8 
71.3 
65.6 
53.8 
42.5 
34.3 


78.0 
77.9 
73.9 
68.3 
68.1 
68.1 
68.8 
71.3 
74.6 
75.2 
76.6 
77.9 


0.183 
0.182 
0.209 
0.317 
0.499 
0.689 
0.799 
0.765 
0.629 
0.414 
0.271 
0.197 


0.129 
0.120 
0.196 
0.318 
0.519 
0.744 
0.858 
0.786 
0.631 
0.404 
0.246 
0.156 


0.101 

0.092 
0.145 
0.217 
0.354 
0.507 
0.590 
0.560 
0.471 
0.304 
0.188 
0.122 


0.028 
0.028 
0.051 
0.101 
0.165 
0.237 
0.268 
0.226 
0.160 
0.100 
0.058 
0.034 


0.082 
0.090 
0.064 
0.100 
0.145 
0.182 
0.209 
0.205 
0.158 
0.110 
0.083 
0.075 


10.0 
10.9 

9.8 
8.8 
7.8 
7.2 
7.2 
6.5 
7.2 
7.7 
8.9 
9.5 


1.83 
1.49 
1.96 
2.21 
2.69 
2.47 
3.70 
2.91 
2.44 
2.37 
1.97 
1.74 


1.27 
1.26 
2.35 
2.97 
3.64 
4.40 
5.11 
4.73 
3.63 
2.65 
1.70 
1.56 


Annual. 


49.5 


51.2 


73.2 














27.77 

























* Wind velocity according to U. S. Weather Bureau at Rochester, N. Y., 1895 to 1906. 
Temperature is given in °F.; relation humidity in per cent; vapor pressure in inches Hg.; 
wind velocity in miles per hr.; and evaporation in inches depth. 



EVAPORATION FROM WATER SURFACES 213 

In computing the evaporation at Mount Hope for January, 
February, March, and October, November, and December, 
the author used the difference between the maximum vapor 
pressure corresponding to the water temperature and a vapor 
pressure for the air above the water, based on the observed 
relative humidity and the water temperature. 

From April to September, inclusive, the evaporation was 
computed by taking the difference between the maximum vapor 
pressure corresponding to the water temperature, and the 
actual vapor pressure in the air as determined from the air 
temperature and the observed relative humidity. 

During the winter months, the water in the floating tubs 
(10-inch fiber pails) was at a surprisingly high temperature, 
presumably due to the pumping of water into the reservoir 
in which the tubs were floating. It is assumed, therefore, that 
the layer of air immediately above the water surface was heated 
to nearly water temperature, and that the most probable value 
of actual vapor pressure, for use in the formula, would be 
secured by applying the relative humidity to the maximum 
vapor pressure at the water temperature rather than at the air 
temperature observed some distance above the water surface. 

The computed evaporation for St. Paul, Minn., is also shown 
in Fig. 144, and indicates satisfactory correspondence with 
actual evaporation observed under similar conditions. 

A study of observed evaporation losses from relatively shal- 
low water in comparison with computed losses leads to the 
conclusion that substantially correct values can be deduced 
from observed meteorological phenomena without resorting 
to actual measurements. The temperature of relatively shallow 
bodies of water follows the air temperature quite closely. Air 
temperature is being observed at several thousand stations 
in the United States, and relative humidity and wind velocity 
are being observed at about 200 stations. Reasonably ac- 
curate base data are, therefore, available for use in computing 
evaporation losses. 



214 ELEMENTS OF HYDROLOGY 

Evaporation from Deep Water. — The temperature of large 
deep bodies of water varies considerably from that of the air. 
In general, the mean annual water temperature is slightly 
higher than the air temperature. The extent to which the 
temperature of lakes varies from the air temperature depends, 
primarily, upon their depth. In summer, the sun's rays with 
the aid of currents set up by waves, warm the water of deep 
lakes to depths of about 150 feet. Below this depth, however, 
the temperature remains substantially uniform, at a little above 
the mean annual air temperature, throughout the year. The 
temperature of the water near the bottom of deep lakes in 
northern latitudes usually remains very close to the temperature 
of maximum density. 

The variation, with depth and season, of the temperature 
of Lake Geneva, Switzerland, and Lake Cochituate, Mass., is 
graphically shown in Fig. 149. Lake Cochituate freezes over, 
whereas Lake Geneva remains open the year around. After 
the entire body of water in the former lake has reached the 
temperature of maximum density, i.e., 39.2° F., the surface 
water cools and, becoming lighter, remains at the surface until 
ice forms. With increasing cold, the ice temperature continues 
to drop and more and more of the layer of water immediately 
below the ice cover cools down to between 32 degrees and 39.2 
degrees. From a few feet below the ice to the bottom of the 
lake the temperature remains at about the point of maximum 
density. As soon as the ice breaks up, in spring, the entire 
body of water soon attains uniform temperature, making it very 
susceptible to circulating currents set up by air movement over 
its surface. As the heat received from the sun increases, the 
surface water heats more rapidly than the deeper layers and, 
being lighter, remains at the top. The result is that by the end 
of mid-summer, the surface of the water usually has at least 
as high a temperature as the air. 

During the season of falling temperature the water remains 
continually warmer than the air, because, as the surface water 



J30 c 



Temperature— Degrees Fahrenheit 
40° 50° 60° 70 c 



80° 



80 



411 



fa 80 
I 



100 



120 



110 



160 



820 







/ 


1 1 7 


■ 1 






/ 


L October 23 / , 


/ ] 


December 19- 
1879 




/ 


y 1879 / / 

! / / 


August 20 
" 1879 






/ 




1 / 

.A—June 
/ 187 


/ 

21 / 
? / 








fc- May H 

I 1879 


/ 


/ 








/ 


/ 










/ 


/ 










/ 

/ 

1 


1/ 

1L 










1 

/ 


\j 










/ 


11 










1 


V 










J i 


/ 










1! 












1 












i is 


VARIATION OF TEMPERATURE 






Hi 


WITH 

DEPTH AND SEASON 

LAKE GENEVA 






f 




SWITZERLANC 


) 






11 

J-1I 1 











Temperature —Degrees Fahrenheit 
40° 50° 60° 70° 




Fig. 149. 



(215) 



216 ELEMENTS OF HYDROLOGY 

cools, it becomes heavier and sinks and is replaced by warmer 
water from below. The circulation thus set up extends deeper 
and deeper. Cooling proceeds throughout a layer of increas- 
ing thickness, eventually reaching the bottom of the lake or 
at least to a depth of about 150 feet below the surface. If cool- 
ing continues after the entire body of water has reached the 
point of maximum density, the surface temperature is rapidly 
reduced and the lake freezes over. 

The currents set up in spring and fall by the change in the 
temperature of relatively deep bodies of water are of consider- 
able importance in connection with public water supplies on 
account of their effect on the character of the water. 

The temperatures determining evaporation from the lake sur- 
face are, of course, the surface water temperatures, but these, 
it will be noted from what has been said above, are intimately 
related to the temperature of the entire body of water, and this 
depends largely upon its depth. The greater the depth of a 
lake the greater the excess of fall evaporation from its surface 
over spring evaporation, at the same temperature. 

When reasonably complete records of both air and surface 
water temperatures, in addition to records of relative humidity 
and wind velocity are at hand, the evaporation from deep water 
can be computed directly from the observed data by means 
of the evaporation formula. Usually, however, no such ob- 
servational data are available. 

In order to meet the need for a measure of evaporation from 
relatively deep bodies of water, and applicable at least to average 
conditions, the author has constructed the curve of Fig. 150, 
on the basis of the available observational data and the known 
general relationship between air and water temperatures. This 
curve, of course, is intended merely to represent an average 
measure which may be applied when specific data are not avail- 
able. 

Fig. 151 shows the evaporation loss from the Lake of the 
Woods as observed by the Manitoba Hydrographic Survey 



EVAPORATION FROM WATER SURFACES 



217 



between 1913 and 1915. This lake has an area of about 1500 
square miles and is about 100 feet deep, in places at its northern 
extremity, but only about 25 feet deep throughout the main 
southern portion. The water temperature at the northern end, 













1 1 1 
































EVAPORATION 

FROM 

WATER, SNOW AND ICE 


















































































70 
























































































































































































■&/. 


Kf 














































vj 


















60 




































/*>• 
















































> J 






























































































<& 


















































~*?f 




'"' 






















50 
























/\ , 
































































































/** 












































.£> 




o 














































































40 
































































/ i/ 


















































/o 




4* 












































V 


















































o" 




































30 














% 
































































































(7°' 




A* 














































4/ 




























































































20 






































































































/■ 
































































































'"' 
















































10 


i/ 




















































































































































































































































ft 



















































12 3 4 

Monthly Evaporation, in Tnehes 

Fig. 150. 



at Keewatin, Ontario, where the measurements were made, 
lagged considerably behind the air temperature, resulting in 
large differences between spring and fall evaporation for the 
same temperature. This condition is likely to prevail on all 



218 



ELEMENTS OF HYDROLOGY 



northern lakes where the rate of change in air temperature 
in spring and fall is great. 

Evaporation from Snow and Ice. — Figs. 150 and 151 also 
give the evaporation from snow and ice. Few observational 



























































































































































































































































TO 




































































































■»■*■ 




















































"•y 


b 
























































Till 










• Aug 






















































































60 
























v7 
























































Jui 


e« 






< 






cs 


v." 




















































*# 






<& 






























































"Sept, 






















































































50 


















47 






















































M 


ay 


»/ 
































































































































1 
























































.A 


>r. 






*c 






































40 














7 






/< 


f 






















































































































* S 




7" 




Monthly Mean Evaporation Observed by 

Manitoba Hydrograph'ic SuTvey 

at Keewatln, Ont. 1913-1915 • 
























*p. 






k 












































































































30 














/k 


r 














































































EVAPORATION 

FROM 

LAKE OF THE WOODS 




















v/j 








































*i 


































20 










* 


d> 
























































';?■ 


^ 






























































r 














































































































<■/ 


























































10 




















































































































































































































































































































it 































































12 3 4 

Monthly Evaporation -Inches 

From Report of Adolph F. Meyer and Arthur V. White, Cons. Engrs. 
mission. 

Fig. 151. 



International Joint Com- 



data are available as a basis for this part of the curve. While 
lakes remain frozen, the incident solar energy is used, primarily, 
in vaporizing the snow and ice cover. This applies equally 
to land areas covered with snow. 



EVAPORATION FROM WATER SURFACES 219 

As early as 1826, Schubler called attention to the high rate 
of evaporation from snow and ice. 

Horton * gives some observations of evaporation from snow 
which check the values indicated by the curve of Fig. 150 very 
well. A loss of .25 inch was recorded during the nine days from 
December 26, 1913, to January 4, 1914. The mean maximum 
temperature during this period was 29.5 degrees, corresponding 
to a monthly mean temperature of about 24 degrees. The re- 
corded evaporation for nine days corresponds to a monthly 
evaporation of .83 inch. The curve of Fig. 150 gives .9 inch 
of evaporation per month at a temperature of 24 degrees. The 
mean wind velocity during the period covered by Horton's 
observations was 7.3 miles per hour. The relative humidity 
recorded by the Weather Bureau for January, 1914, was 78 per 
cent. These values represent approximately the normal con- 
ditions for the Northwest which constitute the basis for the 
curve of Fig. 150. 

Data bearing on the evaporation from snow at high altitudes, 
when subjected to desert winds, are found on page 118 of Water 
Supply Paper No. 294. A rate varying from twice to over 
ten times the evaporation from water is given. Such high values, 
however, are not generally applicable. It may be noted, how- 
ever, that even the author's curves of Fig. 150 indicate that 
"chinook" winds of high temperature and low relative humidity 
can produce high rates of evaporation. At 45 degrees, for ex- 
ample, an extension of the curve would give about 3.4 inches 
evaporation per month from snow and ice surfaces. This is 
based upon the relative humidity prevailing in the Northwest. 
During chinooks, the relative humidity drops very low, so that 
the evaporation would be increased at least 2\ to 3 times. 
The evaporation from a water surface at 32 degrees under sim- 
ilar conditions of humidity would be about 2\ to 3 inches or 
about one third as much as the evaporation from snow and ice. 

The records of the breaking up of the ice on a large number 
* Horton, R. E., Monthly Weather Review, February, 1914, p. 99. 



220 ELEMENTS OF HYDROLOGY 

of lakes indicate that comparatively deep bodies of water 
may be expected to break up in the spring when the monthly 
mean temperature reaches about 83° F., and freeze up in the fall 
when the monthly mean temperature reaches about 20 degrees. 
At the time of break-up there is certain to be a very con- 
siderable reduction in evaporation, because the incident solar 
energy, previously used in vaporizing a surface film of water, 
snow or ice, is absorbed in melting the ice and gradually heat- 
ing the water to a considerable depth. After mid-summer, 
the evaporation from deep water, as previously indicated, will 
be relatively greater than that from shallow water. 



CHAPTER VI 
EVAPORATION FROM LAND AREAS 

As the evaporation from land areas is usually a far more 
important factor in the determination of runoff from a given 
watershed than that from water areas, a clear understanding of 
the variation of such evaporation from land areas with tempera- 
ture, season, rainfall, vegetal cover, topography, soil and subsoil, 
is essential, even though it involves many factors not readily 
evaluated. 

The quantity of water evaporated from land areas depends 
not only on the rates of loss but also on the length of time 
during which evaporation can continue, i.e., it depends not 
only on the rate of evaporation but also on what Horton * 
has aptly termed the "evaporation opportunity" as determined 
by the quantity of moisture available. 

The Rate of Evaporation 

Effect of Temperature. — The most important factor govern- 
ing the rate of evaporation from land areas is the temperature 
of the air and of the moisture subject to evaporation. 

Immediately following a rainstorm, the rate of loss from land 
areas approximates the rate of loss from shallow water. If 
the ground was quite dry the soil temperature is higher than 
the air temperature and the rate of loss even greater than that 
from water. As evaporation proceeds and the free moisture 
on the surface of vegetation and bare earth disappears, the rate 
of loss gradually becomes lessened. This reduction in the rate 
of evaporation is more rapid at higher than at lower temperatures 
so that although at first, after a rainstorm, the rate of evapora- 

* Horton, R. E., Trans. Am. Soc. C. E., Vol. LXXIX, p. 1171. 

221 



222 



ELEMENTS OF HYDROLOGY 



Hon from land varies with temperature, the same as the rate of 
evaporation from water, it does not follow that the quantity 
evaporated per day or per month is directly proportional to such 
rate of evaporation. 

Although air temperature does not determine the amount of 
precipitation lost in evaporation from land areas it is nevertheless 
an important index to the rate. Records of maximum, minimum, 



J 10 



OJ108 



<=) 80 



3 

ts 70 

u 

I 

£ 60 



































DAILY VARIATION IN TEMPERATURE 

OF AIR SOIL AND WATER 

AT 

DAVIS, CALIFORNIA 

JULY, 1910 

DATA FROM BULLETIN NO. 248 
OFFICE OF EXPERIMENT STATIONS 
U.S. DEPARTMENT OF AGRICULTURE 














































y 
















Soil at i 


in. dept 


h 
















^Watei 


at 6 in. 


leptli 


























SoU a 


t&in. d 


epth/ 




















^-Air 





































6 


s 


10 12 2 


1 


6 


P.M. 




Midnight 
Fig. 152. 




A.M. 



and mean daily, monthly, and annual air temperature are avail- 
able for nearly 6000 Weather Bureau stations in the United 
States. A determination of the temperature of the moisture 
that evaporates from land areas must be based on the observed 
air temperatures. Fig. 152 shows the daily variation in the 
temperature of the air, water, and dry- soil at Davis, Califor- 
nia, on July 12 to 13, 1910. The mean temperature of the 
air for the day was 70.4 degrees. The mean temperature of 
the dry soil one half inch below the surface was 84.9 degrees 



EVAPORATION FROM LAND AREAS 



223 



and at six inches below the surface it was 86.8 degrees. The 
mean temperature of the water at one half inch below the sur- 
face was 78.9 degrees decreasing about one degree to six inches 
depth. The range in air temperature during the day was 
47| degrees while the range in water temperature was only 
20 degrees. The range in temperature of the soil at one half 
inch depth was 64 degrees and at six inches depth 12 degrees. 
At about 2\ inches below the surface, the range of soil temperature 
was substantially equal to the range in water temperature. 




00 



TEMPERATURES OF AIR, SOIL, AND WATER 

RIVERSIDE, CALIFORNIA 

AUGUST, 1905 

From Bulletin No. 177 

Office of Experiment Stations 

U.S. Department of Agriculture 



Time - Days 
Fig. 153. 



w 



Additional observations showing temperatures of air, soil, 
and water are shown in Fig. 153. On the whole, the irrigation 
investigations indicate that the temperature of dry soil in the 
sun is higher and the temperature of moist soil is lower, in summer, 
than that of the overlying air. 

Foreign observations on the temperature of the soil and of 
the air in the forest and in the open field indicate that the 
mean air temperature in the forest is about two degrees lower 
in summer, and that the mean annual temperature averages 
about one degree lower. The difference between the air tem- 
perature in the forest and in the open is graphically shown in 



224 



ELEMENTS OF HYDROLOGY 



Fig. 154. As the result of this difference in air temperature, 
a difference is also noticeable in the temperature of the soil 
in the forest. This is shown in Fig. 155. 

From the surface of the ground, the air temperature in 
the forest rapidly increases, reaching a value a short distance 
above the tree-tops substantially equal to the air temperature 
in the open. 



b+3 

S +% 
2 +1 
g> o 
e -i 

' -2 
O -3 

E -5 
a -6 

a -1 





It 


aximum^ 























•*•- 


1 




"" 




~~^ 






k " 




" 




















^«^_ 


. 


















* 










| % 






/ 








Mil 


niiiim ' 










S 
















\ 


































































































































A M J J 
Months 



A S O N D 



Fig. 154. 



Data from Bid. No. 7, Forestry Div., U. S. Dept. of Aijr. 

Difference in Air Temperatures, Woods and Open Fields. 

fe+3 



to -9 
5-10 

























1 






















m^ 




















cTTT 








V, 






[)fl 


itli 11 ins. 




j> 


-" 








\\ 


V 








y/ 


,' 












^ \ 


^-D 


Jp th 


4-itJ '/ 


'/ t . 














\\ 








// 


s 
















V 


-^ 


.^ 
























'/* 


S 


iiiu 


re 














\. 



















































































J F M 



A M J J A 
Months 



S O N D 



Fig. 155. 



Data from Bui. No. 7, Forestry Div., U. S. Dept. of Agr. 

Difference in Soil Temperatures, Woods and Open Fields. 



In general the daily and monthly mean air temperature 
may be taken as the best available index to the mean rate of 
evaporation from land areas. 

Effect of Relative Humidity. — The effect of relative humidity 
on the rate of evaporation from land areas is the same as its 
effect on the evaporation from water surfaces, namely, the 
rate of evaporation varies substantially as the saturation deficit. 
German observations * indicate that the actual moisture content 
of the air in the forest is only about one per cent greater than 

* Reported in Bulletin No. 7, Forestry Division, U. S. Department of 
Agriculture, p. 102. 



EVAPORATION FROM LAND AREAS 225 

in the open, but because of the lower temperature, the relative 
humidity is from two to three per cent- greater than in the open. 

Effect of Vegetation. — All forms of vegetation, particu- 
larly forests, shade the ground to a certain extent and con- 
sequently reduce the rate of evaporation of free moisture. 

Transeau * gives the following relative rates of evaporation 
observed at Cold Spring Harbor, Long Island. 

Per cent 

Bare sand and gravel slide 100 

Open garden plot with low herbaceous vegetation 80 to 100 

Upper beach areas 80 to 90 

Light forest on gravel soil 50 to 70 

Dense forest with abundant undergrowth 35 to 40 

Dense ravine forest with abundant herbaceous vegetation 13 

Dense swamp forest with abundant undergrowth and 

water near surface 10 

Fresh-water marsh 45 

The evaporation was measured with Livingston porous-cup 
atmometers placed about four inches above the surface of the 
ground. 

The rates given are, of course, merely relative and represent 
rates of evaporation of free moisture. According to these obser- 
vations, the evaporation from the water surface of a L*esh-water 
marsh is reduced to about one half by the presence of the 
grasses. Open forests appear to effect an equal reduction and 
dense forests, with abundant undergrowth, reduce the evapora- 
tion of free moisture to about one quarter of that in the open. 
The effect considered here is, of course, the sum total of the 
effect of vegetation, including reduction in temperature and 
wind and increase in humidity, but not the effect of vegetation 
in intercepting rainfall. Practically no watershed, however, 
has any large area free from all vegetation. The effect of 
forests in reducing the rate of evaporation of free moisture 
must be based upon a comparison of evaporation in the forest 
with evaporation from the ordinary cultivated field, grass 
land, or brush- and weed-covered watershed. 

* Transeau, E. N., Botanical Gazette, April, 1908, p. 218. 



226 ELEMENTS OF HYDROLOGY 

German observations * indicate that the evaporation from 
an evaporation pan in dense woods is 44 per cent and from young 
trees is 80 per cent of that in the bare, open field. 

Considering the rate of evaporation from the bare ground 
surface at a given mean temperature as 1.0, the rate of evapo- 
ration of free moisture from the ground in grain fields may ten- 
tatively be taken as .8; for grass land .7; for light forests, 
brush, and second growth .6; and for dense forests with abundant 
herbaceous vegetation from .2 to .4. 

The Evaporation Opportunity 

The opportunity for a given rate of evaporation to continue 
is determined by the available moisture supply. 

Effect of Precipitation. — The available moisture is influenced 
most largely by the amount, rate, and character of the pre- 
cipitation that falls on the given watershed. Frequent, light 
showers that keep the surface soil and the surface of the bare 
ground and of vegetation moist, permit of the greatest evapo- 
ration. Slow, steady rains favor percolation. Torrential rains 
favor surface runoff. For equal precipitation, then, that which 
falls as light, frequent showers, provides the greatest oppor- 
tunity for evaporation. 

The character of the precipitation also has an important 
influence on the evaporation opportunity. During the winter 
in the Northwest, when most of the precipitation falls as snow 
and the ground remains covered with snow and ice for several 
months, the evaporation opportunity on the land area of a 
watershed is at least equal to that on the water area. If the 
watershed is covered with a dense coniferous forest, the evapo- 
ration opportunity will exceed that for the water area, because 
the snow lodges on the branches of all evergreen trees and greatly 
increases the area subject to evaporation loss, besides permit- 
ting increased day temperatures in the forest. 

* Reported in Bui. No. 7, Forestry Div., U. S. Dep't of Agriculture, p. 102. 



EVAPORATION FROM LAND AREAS 



227 



Effect of Interception. — During the summer months when the 
precipitation falls as rain, a greatly varying, but considerable, 
portion of it is intercepted by trees, shrubs, and other vegetation 
and re-evaporated without ever reaching the ground. A small 
portion of the rain caught by the tree tops runs down the trunk. 

The quantity of precipitation intercepted by vegetation 
varies largely with the quantity of rain that falls in a given 




Courtesy Am. Soc. C. E. 
Fig. 15(i. — Interception of Snowfall by Evergreen Forest. 

time. A much larger percentage is lost out of small showers 
than out of heavy rains. Deciduous trees intercept much more 
rain during the growing season when in leaf, than in the winter, 
when the leaves have fallen. Coniferous trees, as above men- 
tioned, intercept large quantities of snow. A typical western 
evergreen forest with a heavy snowfall lodged on the branches 
is shown in Fig. 156. 

Unfortunately the available data on the subject of inter- 



228 ELEMENTS OF HYDROLOGY 

ception consist mainly of percentages of precipitation intercepted 
without reference to actual interception for each rainfall. 
The average interception at 16 German stations * was 25 per 
cent; the average of 12 years Swiss observations was 16 cent. 
M. Fautrat found 40 per cent intercepted for annual precipita- 
tion of about 28 to 30 inches quite uniformly distributed 
through the year. Riegler found 60 per cent intercepted by 
spruce and 22 per cent by beech, oak, and maple. 

Interception is virtually constant for each shower which is 
sufficient to thoroughly wet the vegetation. Until more com- 
plete observational data are available the accurate evaluation 
of the amount of precipitation intercepted by various forms 
of vegetation would appear impossible. 

Effect of Percolation. — For a given precipitation, the greater 
the facility for percolation, the less the opportunity for evap- 
oration. Percolation is favored by a slow, steady precipitation, 
pervious soil, and flat slopes. On some pervious watersheds 
with relatively steep slopes, however, the surface topography 
is such as to form numerous, small, wet-weather lakes and 
ponds that overflow only during exceptional floods. On such 
watersheds the percolation is always great, and all forms of 
vegetation reduce percolation by absorbing a large amount of 
capillary water which would otherwise be held over from one 
rain to the next, and would permit most of the rainfall absorbed 
by the surface soil to percolate down to the water-table instead 
of first replenishing the capillary water used by the plants. 

King f found the following rates of percolation through 
columns of sand and soil having a cross-section of .1 square foot 
and 14 inches long, when kept covered with 2 inches of water: 

In No. 40 1 sand, percolation at the rate of 301 inches per day. 
In No. 100 § " " " 39.7 

In clay loam " " 1.6 

* Reported in Bui. No. 7, Forestry Div., U. S. Dep't of Agriculture, p. 102. 
f King, F. H., Nineteenth Annual Report, U. S. Geological Survey. 
t No. 40 sand, effective diameter, 0.185 mm. 
§ No. 100 " " " 0.083 mm. 



EVAPORATION FROM LAND AREAS 



229 



Wollny * found the following rates of percolation in various 
soils : 

TABLE 28. — RATES OF PERCOLATION (Wollny) 





millimeters 


Water sank to the given depth 


Size of soil grain, 


After 
5 min. 


After 
10 min. 


After 
15 min. 


After 
25 min. 


After 
45 min. 


After 
65 min. 


After 
120 min. 


0.01 to 0.071 


cm. 

8.8 
18.0 
28.3 
45.0 
84.0 
11.0 


cm. 

12.8 
27.0 
48.0 
82.0 


cm. 

16.2 

37.0 

65.0 

110.0 


cm. 

21.3 
52.5 
96.0 


cm. 

30.0 
79.0 


cm. 

36.7 
103.0 


cm. 
52.0 


0.071 to 0.114. 




0.114 to 0.195 






0.175 to 0.2... 








0.25 to 0.50 










Mixture of various grains 


19.0 


24.5 


33.2 


50.8 


65.5 


106.0 



Wollny's experiments were made with soil of varying grain, 
placed in tubes 110 cm. deep, the water dropping constantly 
on top of the soil column. 

Although none but the most exceptional watersheds of small 
area would have a surface covering of coarse sand, yet the differ- 
ence between clay and sandy soils in facilitating percolation 
is very marked. 

The rate of percolation is also affected by the initial con- 
dition of "the soil. When the upper layers become nearly air 
dry to any considerable depth, the pore space becomes so filled 
with air as to retard, greatly, the entrance of water. This is 
particularly true of the denser soils, the individual pore spaces 
of which are relatively small, even though their moisture-hold- 
ing capacity may exceed that of the coarser sands. The large, 
deep cracks that form in the clay soils when these are thoroughly 
sun-baked compensate, in some measure, for the detrimental 
effects upon porosity of the excessive drying of such soils. 

Cultivation, that is, tillage as opposed to cropping, is a great 
aid to percolation, and unless tilled fields are immediately packed 
by exceptional, beating rains, cultivation ranks among the most 
important factors promoting percolation. 

* Wollny, E., Experiments reported in Bui. No. 7, U. S. Dep't of Agri- 
culture, Forestry Division. 



230 



ELEMENTS OF HYDROLOGY 



Fig. 157 shows the effect of cultivation in reducing evapo- 
ration from the soil. In this case moisture was supplied by ir- 
rigation instead of precipitation, but the effect is the same. It 
will be noted that about 50 per cent of the 28 day loss occurred 
in the first three days. 

1.75 



1.50 



1.25 



81.00 



.75 & 



.50 























1 


Uncultivated 










1 
1 


Cultiv 


itedv^,^. 




a 

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EFFECT OF CULTIVATION 

ON SOIL EVAPORATION 

RENO. NEVADA 








Da 

oai 

U.S. 


JUNE 
ta from B 
:e of Expo 
Dopartmei 


1909 
llletin No. 

■inii-ut Sta 
it of Agric 


248 

tiona 
ulture 





12 16 

Time - Days 

Fig. 157. 



38 



Cultivation not only breaks up the sun-baked surface layer 
so as to reduce surface runoff and aid percolation into the upper 
layers of soil, but, by forming a mulch, it reduces evaporation. 
In this way cultivation preserves the capillary water in the soil 
and permits the additional percolating precipitation to become 
gravity water and move downward toward the water table 
where it is usually safe from evaporation. 

For any given character of soil, a cultivated watershed which 
is permitted to lie fallow would yield the best seepage flow. 
Fall plowing on cultivated watersheds is particularly bene- 
ficial, and may result in the storage of a larger quantitjr of water 
during the fall, winter, and spring than that used in transpira- 
tion during the following growing season. 



EVAPORATION FROM LAND AREAS 



231 



Depth of Percolation and Rate of Return of Moisture by 
Capillarity. — Another factor which affects the evaporation 
opportunity from a given watershed is the moisture-holding 
capacity of the soil, and the depth to which the percolating 
waters pass, and also the ability of each particular soil to raise 



Black 
Loam 



Gravelly 
Loam 



Sandy 
Gravel 



Sand 



.Tine 
Sand 



•>: 




5 10 15 20 35 

Per cent of Moisture by Weight 

Fig. 158. 



water to the surface again by capillary action. The finer the 
soil and the more humus it contains the greater its capillary 
power. This is well shown in Fig. 158. Capillary action is 
also facilitated by the rotted fibers of dead roots, which in 
some forms of vegetation penetrate to considerable depth. 
Hazen * expressed the relationship between size of soil grain 
* Hazen, Allen, Report Mass. State Board of Health, 1892, p. 541. 



232 



ELEMENTS OF HYDROLOGY 



and height to which water will be lifted by capillarity in suffi- 
cient quantity to prevent the circulation of air, in the following 



h = 



1.5 



when h is the lift and d the 



approximate formula : ,«, - - , 2 

effective size of soil grain, both in millimeters. 

The capillary lift of different soils is also of importance in 
connection with the life of wooden sub-structures, such as pile 
foundations, occasionally exposed by low water. 

Experimenting on a series of cylinders, each having an area 
of cross-section of .1 square foot, and filled with a mixture of 
sand in approximately natural proportions, grains varying in 
size from No. 100 to No. 20, King * found the following rates 
of evaporation for capillary lifts varying from 6 to 30 inches. 
The temperature of the air in the laboratory where the experi- 
ment was conducted was about 70° Fahr., and the relative 
humidity is reported to have been very low. 



Capillary lift, 

in inches above 

ground-water 

table 


Evaporation, 

in inches per 

month 


6 
12 
18 
24 
30 


3.42 
3 34 
2.39 
1.04 
0.58 



It is worthy of note that the maximum evaporation given in 
the above tabulation is only about one half of what might be 
expected from a free water surface under the conditions of tem- 
perature and humidity stated. It is probable that if evaporation 
had been accelerated, capillarity would have shown itself equal 
to raising the moisture to the surface at a more rapid rate than 
that found by the experiment for capillary lifts of only a few 
inches. 

The rates of evaporation given for a capillary lift of 30 inches 
indicate that when the water-table for the particular soil 

* King, F. H., 19th Annual Report, U. S. Geological Survey. 



EVAPORATION FROM LAND AREAS 



233 



used in King's experiments drops to more than 4 or 5 feet be- 
low the surface of the ground, evaporation is reduced to a very 
small quantity. 

Lee * states that the capillary lift is practically limited to 
four feet in coarse sandy soil, and to eight feet in fine sandy 
or clayey soil. 





1 

2 
3 
A 
5 
6 


"I 


Total Evaporation plus Transpiration -Tnches Depth 
3 10 15 20 25 30 35 40 45 






















6»A~ 


7 

Losses 
October 1 


•1 

between 
and March 


°i 

31 




S~ { 








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/ j Losses be 
y/^ April 1 and 


°6 

tween 
Sept. 30 




4. 






4 












.2 / 


•3 

o2 




y*3 




















RELATION BETWEEN 

CAPILLARY LIFT 

AND 

EVAPORATION PLUS 

TRANSPIRATION LOSS 

CALIFORNIA 

Data from Water Supply Paper No. 294 














R 





















Fig. 159. 



The results of some of Lee's observations on evaporation 
and transpiration losses from the Owen's Valley, California, 
soils are summarized in the curves of Fig. 159. The deviation 
of the observed losses from Tanks Nos. 1, 2, and 6 from the 
straight line relationship shown by the other observations results 
primarily from the fact that the surface of Tank No. 1 consisted 
of bare sand, No. 2 had but scattered growth of salt grass, 
and No. 6 had a vigorous growth of grass. 

* Lee, Charles H., Trans. Am. Soc. C. E., Vol. LXXVIII, p. 148, and U. S. 

Geological Survey, Water Supply Paper No. 294, p. 59. 



234 ELEMENTS OF HYDROLOGY 

McGee * states: "While the effectiveness of capillary move- 
ment varies with the texture and structure of soil and subsoil 
and underlying rock, it may be said broadly that under average 
conditions capillarity acts freely to four or five feet in depth, 
fairly to ten feet, and slowly to thirty or more feet." 

Burr, Hering and Freeman concluded from their Long Island 
studies f that water percolating to eight feet in fine sand and 
three or four feet in coarse sand will not return. 

Slichter J found that while the evaporation from a water sur- 
face in Kansas from August 6 to September 3, 1905, was 
10.90 inches, the evaporation from cultivated soil with a water 
table within one foot of the surface was 4.88 inches and from 
uncultivated soil with the water-table at the same level, 5.83 
inches. The evaporation from the soil for a capillary lift of 
two feet was 2.23 inches and for a capillary lift of three feet 
the evaporation was reduced to .80 inch. 

Professor Whitney § found that certain soils in southern 
California had such extensive capillary power as to be able 
to draw sufficient water from a depth of twenty feet or more 
to mature crops on one inch of rainfall between May and Sep- 
tember, while neighboring soils were practically barren. 

Extensive capillary action, coupled with excessive evaporation, 
results in the bringing of large quantities of salts to the surface 
of the ground and in the formation of what is known as "alkali" 
soil. 

Briggs and Lapham || found that moist sandy soil exerted a 
capillary lift of 65 inches. 

Stewart H found moist, sandy, rich soils to exert capillary 
lifts of from 45 inches to 70 inches. 

* McGee, W. G., 1911 Yearbook of the Department of Agriculture, p. 482. 

f Report of the Commission on Additional Water Supply for the City of 
New York, 1903, p. 756. 

t Slichter, C. S., Eng. News, July 5, 1906. 

§ Whitney, Wilton, Yearbook U. S. Dep't of Agriculture, 1897, p. 432. 

|| Bulletin No. 19, Bureau of Water, U. S. Dep't of Agriculture, 1902, p. 26. 

If Stewart, J. B., Thesis "Capillary Use of Water in Soils," Michigan, 
Agricultural College, 1901. 



EVAPORATION FROM LAND AREAS 235 

Not only the extent of the capillary lift, however, but also 
the rate of movement of water for given capillary lifts is im- 
portant. Fine, clayey soils exert a great capillary lift, but the 
interstices are so small as to offer such great resistance to flow 
that the maximum rate of movement of water is relatively small. 
For low capillary lifts, sandy soils will supply much more water 
at the surface of the ground for evaporation and transpiration 
than clayey soils. On the other hand, clayey soils will supply 
moisture at the surface even when the water table has dropped 
far out of reach of sandy soils. Soils containing considerable 
humus not only exert a strong capillary lift but permit rapid 
movement of the water through the pore space. 

The depth to the water table, then, is an important factor 
in determining the evaporation opportunity. 

Depth of Water-table. — The average depth of the water- 
table in central United States is well shown by Dr. McGee's * 
investigations on the depth to the water surface in wells. On 
the basis of reports received for 7498 wells, it appears that the 
average depth to the water surface, — which is probably two 
or three feet below the water-table of the surrounding country 
— varies from 17.9 feet in Indiana to 22.6 feet in Wisconsin, 
averaging 22.2 feet for the entire central portion of the United 
States. About half of the wells reported no change in elevation 
of the water surface within the memory of the reporter. The 
average of those reporting a change during the period within 
the memory of the reporter, which averaged about 25 years, 
indicated a lowering in the water-table, varying from about 
one foot in Missouri, to nearly four feet in Wisconsin and Min- 
nesota. Inasmuch as the data compiled by Dr. McGee appear 
to be based merely on testimony as to changes and are not the 
result of observations regularly reported during the course of 
25 years, it would appear that the water surface in the wells 
must have remained substantially stationary. An increase 

* McGee, W. J., 1911 Yearbook of the Dep't of Agriculture, pp. 479 to 
490. 



236 ELEMENTS OF HYDROLOGY 

in settlement results almost invariably in the improvement of 
water supplies. This usually means drilled wells and often 
sufficient pumping to considerably lower the water-table im- 
mediately adjacent to the wells. It is doubtful whether the 
data presented by Dr. McGee warrant the conclusion that 
the water-table throughout the Mississippi Valley has been 
materially lowered during the past 25 years. 

Effect of Vegetation. — Vegetation affects the evaporation 
opportunity in several ways. By using some of the capillary 
water, plants reduce the evaporation opportunity, so far as the 
soil is concerned, but through interception of precipitation, as 
previously explained, they increase the evaporation opportunity. 

In so far as plants use water for their growth and in this way 
keep the moisture content of the soil lower than it would other- 
wise be, they reduce percolation. In so far as all forms of 
vegetation present some obstruction to the flow of water over 
the surface of the ground plants aid percolation. Leaf mold 
in the forest presents a pervious surface to precipitation. A 
layer of undecayed leaves, on the other hand, presents an almost 
impervious surface. Leaf mold has great moisture holding 
capacity. In consequence, the surface soil in the forest is 
usually quite moist and the evaporation opportunity is in- 
creased, although the rate of evaporation, as previously stated, 
is considerably reduced by the shade of the forest. Ample 
moisture supply in the surface soil fosters the growth of luxu- 
riant herbaceous vegetation with the consequent increased water 
consumption in transpiration, except in dense coniferous forests 
and those deciduous forests of tall dense timber that prevent 
the entrance of sufficient light to support small vegetation. 

Wollny found that a grass cover reduced percolation below 
the root level to practically half of that permitted by bare 
soil. 

Ebermayer found that young beech and spruce trees reduced 
the amount of water found to percolate below the four-foot 
level. In his experiments, only about two inches, out of a total 



EVAPORATION FROM LAND AREAS 237 

of 37.6 inches of precipitation, percolated below this level. 
During the winter, the percolation through the experimental 
boxes which contained young deciduous trees was substantially 
equal to that for the boxes which contained bare soil, but 
during the summer, the percolation was much less for the boxes 
which contained the trees. 

The effects of vegetation on percolation, found by Wollny 
and Ebermayer, are undoubtedly due to the amount of capillary 
water used by the plants rather than to any surface effect in 
obstructing percolation. 

Ebermayer found that during summer and fall a loamy, 
sand soil contained about 20 per cent of moisture in the open, 
fallow field, as against 15 per cent in the forest at depths of 
from 16 to 30 inches. More moisture, however, was found 
in the upper few inches of the forest soil. 

In a field in which the water-table was from 5 to 8^ feet 
below the surface of the ground, and in which alternate strips 
of land had been planted to corn, King found the plane of 
saturation depressed materially under the corn. During the 
succeeding season, corn was planted in the strips which had 
lain fallow the previous season and the water-table was again 
found depressed by the vegetation. 

The magnitude of the several effects of vegetation on the 
evaporation opportunity usually depends upon the character 
of the watershed and the character of the vegetation. 

Effect of Drainage. — The principal effect of both tile and 
open ditch drainage on the evaporation loss from land areas 
is to reduce the evaporation opportunity. The drainage of 
land presupposes an excess of moisture on the surface of the 
ground and in the upper few feet of soil — the layer from which 
the evaporating water is primarily drawn. By removing both 
wet-weather and permanent ponds and pools, by lowering the 
water-table, and by eliminating all gravity water from the upper 
layers of soil, drainage reduces the opportunity for evaporation 
losses from land areas. 



238 



ELEMENTS OF HYDROLOGY 



Other effects of drainage will be considered in discussing stream 
flow. 

Observed Evaporation Losses from Land Areas. — Scientific 
literature affords few records of actual measured evaporation 
losses from land areas. Most of the available data do not 
differentiate between evaporation and transpiration. As these 
two losses do not vary in the same way with the changing seasons 
they should be separately considered. 

Irrigation Investigations. — Among the best available data 
on evaporation losses are those published by the U. S. Depart- 




2 4 6 

Evaporation - Inches per Month 



Fig. 160. — Relation between Soil Moisture and Evaporation, California. 



nient of Agriculture and similar departments of several states.* 
Although surface irrigation and precipitation differ in important 
respects, yet the data gathered in connection with irrigation 
investigations are of great assistance in gaining an under- 
standing of the factors that influence evaporation from land 

* For example: Bulletin 177, Evaporation Losses in Irrigation, and Bulle- 
tin 248, Evaporation from Irrigated Soils, Office of Experiment Stations, 
U. S. Dep't of Agriculture. 



EVAPORATION FROM LAND AREAS 



239 



areas and the amount of evaporation that occurs under certain 
conditions. 

Fig. 160 shows the relation between the moisture available 
in the soil and the quantity evaporated.* The soil experimented 
with was a well-pulverized, sandy loam. The rapid decrease 
in the rate of evaporation after the percentage of moisture 
dropped below 10 is significant. When the moisture content 
of this particular soil dropped below 3.5 per cent of its dry 
weight, evaporation practically ceased. 



0.50 



'0.40 



0.30 



30.30 



0.10 



0.00 



EVAPORATION FROM 

BARE SOIL AND WATER SURFACE 

CALDWELL, IDAHO 

June, 1909 




0.50 



a 0.40 



1 0.30 



10.10 



0.00 



Fig. 161. 




Relative Evaporation from Land and Water. — Figs. 161 and 
162 show the rates of evaporation from bare soil and from a 
water surface, in the same locality. The evaporation from 
the clay soil at Caldwell, Idaho, for about three days following 
the application of irrigation water, actually exceeded the evap- 
oration from a water surface. This is undoubtedly due to the 
fact that the irrigation water was held so long at the surface of 
the clay soil, and the temperature of the soil at the beginning 
of the experiment was very much higher than the temperature 
of the water in the evaporation tank. In the case of the sandy 
soil at Reno, Nevada, the evaporation loss from the soil from 

* The data used in constructing this curve were taken from Bulletin No. 
177. Office of Experiment Stations, U. S. Dep't of Agriculture. 



240 ELEMENTS OF HYDROLOGY 

the very beginning was less than the loss from the water sur- 
face. This sandy soil absorbed six inches of surface irrigation 
in a few hours and was sufficiently dry to permit surface culti- 
vation after 24 hours, whereas the clay soil at Caldwell could 
not be cultivated until after three days. A significant fact 
brought out by these diagrams is the fact that about half of 
the evaporation loss from the soil occurred in the first three 
days after irrigation. Other records of the office of Experiments 
Stations point to the same conclusion. 

Some of the actual measured evaporation losses from land 
areas, determined by the U. S. Department of Agriculture in 
its irrigation investigations, together with such other relevant 
• data as were available, are summarized in Table 29. 

Effect of Character of Soils. — The soils used in the experi- 
ments at Wenatchee, Reno, Sunnyside, and Caldwell contained 
substantially the same amount of initial moisture and received 
practically the same amount of water through surface irrigation 
and precipitation. The coarser sandy soils at Wenatchee and 
Reno permitted rapid percolation, as indicated by the high 
moisture content in the bottom layers of the soil at the end 
of the experiment. This reduced the moisture content in the 
upper layers and consequently reduced the subsequent evapora- 
tion loss. The clay soil at Caldwell, on the other hand, re- 
tarded percolation, as indicated by the fact that it required 20^ 
hours to absorb six inches of irrigation water, ^and then per- 
mitted an evaporation loss of about one quarter of that from 
the water surface. The evaporation loss from the Williston 
gumbo amounted to nearly half that from a water surface, 
and the Bozeman soil with its great moisture-holding capac- 
ity permitted two thirds as much evaporation in 28 days 
as a water surface in the same locality. The Bozeman soil 
was of extremely fine texture, and exerted such a great capillary 
lift that the moisture content at the close of the experiment was 
substantially uniform throughout. 



EVAPORATION FROM LAND AREAS 



241 



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CHAPTER VII 
TRANSPIRATION 

Definition. — Transpiration is the process of vaporization of 
water from the breathing pores, or stomata, of leaf and other 
vegetable surfaces. 

Effect of Temperature. — Clements * states that 95 per cent 
of the light energy absorbed by the chloroplast of the leaf is 
converted into heat. Most of this heat is used in the vapor- 
ization of the water from the dilute solutions of mineral salts 
drawn into plants through the root system and used in building 
up plant tissue. The moisture retained in the plant tissues 
themselves is an inconsequential factor in the disposal of pre- 
cipitation. 

In discussing evaporation, it was indicated that, other factors 
remaining constant, the rate of evaporation from shallow water 
is approximately doubled for every 18 degrees increase in tem- 
perature. Van't Hoff and Arrhenius have enunciated the prin- 
ciple that most chemical reactions and physiological processes 
double in activity for every similar increase in temperature. 
This law has been found, by experiment, to apply to a number 
of phases of plant activity. It has, for example, been found to 
be substantially correct for the rate of fixation of carbon dioxide 
by plants in sunlight; and, inasmuch as transpiration occurs 
during the process of carbon dioxide assimilation, when the 
stomata open in the sunlight, it is reasonable to conclude that 
the rate of transpiration, in so far as it is dependent on temper- 
ature, substantially follows Van't Hoff 's law. 

In applying this law, however, it is necessary to decide on a 
temperature at which plant activity begins. Koppen regards all 

* Clements, F. E., Plant Physiology and Ecology, p. 85. 
242 



TRANSPIRATION 



243 




244 



ELEMENTS OF HYDROLOGY 



monthly mean temperatures less than 48 degrees as included in 
the period of rest of plants. Other scientists hold that the pro- 
toplasmic contents of vegetable cells are inactive while the tem- 
perature is below 6° C. (42.8° F.). 

Fig. 163 shows the United States divided into different vegetal 
regions based upon periods of growth and rest as determined by 
temperature alone, without reference to available moisture. 

In temperate latitudes, when there is a lack of precipitation 
or irrigation, monthly mean temperatures of more than 72 degrees 
constitute a period of summer rest for most plants. When suf- 
ficient moisture is present, they constitute a period of ripening for 
southern fruits, and, when there is an abundance of moisture, 
these high temperatures constitute the period of sub-tropical 
growth. 



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40 50 



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60 70 80 80 70 60 

Monthly Mean Air Temperature,— Degrees,, Fahrenheit. 
March to July August to November 

Fig. 164. 



/ Fig. 164 shows the author's base curve of transpiration founded 
mainly upon the above expressed effect of temperature on tran- 
spiration. This curve is used as the basis for estimating changes 
in monthly transpiration, on a given watershed, with changes in 
monthly mean air temperature, without reference to available 
moisture. 

i Figs. 165 and 166 show the relation between maximum and 
minimum daily temperatures and the growth of corn. The rate 



TRANSPIRATION 



245 



of growth is approximately doubled for an increase of 15 degrees 
in temperature. 

Botanists agree that every plant has its optimum moisture, 
temperature, and light conditions under which it makes its best 
growth. When there is an excess of moisture, crop yields are 





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Maximum 'IVuiitcraturt' 
































Growth of Corn 
































1 1 1 1 1 1 1 1 































Fig. 165. — Relation between Maximum Temperature and Daily Growth of 
Corn in Pennsylvania, July 5-27, 1889 (after Smith). 





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Growth of Corn 




























































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Fig. 166. — Relation between Minimum Temperature and Nocturnal Growth 
of Corn in Pennsylvania, July 5-27, 1889 (after Smith). 



determined largely by temperature. When rainfall is sufficient 
and the temperature is too low for best growth, sunshine becomes 
the most important factor. Heat cannot replace sunlight in the 
growth of vegetation, but sunlight can partly replace heat. When 
temperature and sunshine are sufficient, crop yields depend 
mostly on rainfall. 



246 ELEMENTS OF HYDROLOGY 

Effect of Humidity. — All the experiments which have been 
made upon the water requirement of plants, for a given amount 
of growth, indicate that more water is used, per pound of dry 
material produced, by plants growing in dry air than by those 
growing in moist air The experiments of Montgomery and 
Kiesselbach,* on corn grown in greenhouses, indicate that the 
amount of water required per pound of dry material produced 
is proportional to the evaporation from a water surface, which, 
it has already been shown, is proportional to the saturation 
deficit of the air. The plants grown in the humid atmosphere 
(58 per cent relative humidity during daylight hours) produced 
about 25 per cent more dry matter and used about 12 per cent 
less water than those which grew in the dry atmosphere (37 per 
cent relative humidity during the day). From an engineering 
viewpoint the effect of relative humidity on the total amount of 
water used, rather than on the water used per pound of dry 
matter produced, is the effect desired. This, however, does not 
appear to have been determined. It is probable, however, that 
the increased growth resulting from increased humidity causes a 
total water loss in a humid atmosphere about equal to that in 
a moderately dry atmosphere provided a reasonably sufficient 
amount of soil moisture is available for the plant to use. 

Effect of Wind. — By hastening the removal of vapor from the 
leaf surfaces from which it is being transpired, air movement 
results in increased transpiration. 

Effect of Light. — Transpiration is practically limited to the 
daylight hours. In this respect it differs from evaporation, which 
continues through the night at a rate determined, primarily, by 
the temperature. This is well shown by Fig. 167 which gives 
a continuous record of the transpiration of wheat, observed at 
Akron, Colo., in July 14-15, 1912, and reported in " Journal of 
Agricultural Research," Vol. 5, No. 3. The loss during the night 
was about one tenth of the loss during the day, which reached its 

* Montgomery, E. G., and Kiesselbach, T. A., Nebraska Agricultural 
Experiment Station, Bulletin 128, 1912. 



TRANSPIRATION 



247 



maximum at noon. The loss during the night was also substan- 
tially uniform. 

As the leaves of plants turn toward the sun, it is immaterial 
what the slope of the ground is,* or what the angle of the sun 
is during the daylight hours except in so far as the longer path of 




10 12 2 
Midnight 



Fig. 167. — Variation of Transpiration of Wheat with Daylight, 
July 14-15, 1912. 

the sun's rays through the atmosphere during the early morning 
and late afternoon has an effect on the absorption of a part of 
the sun's energy. The following table shows the proportionate 
amount of solar radiation reaching the earth for various angular 
altitudes of the sun, considering the amount reaching the outer 
atmosphere as 1.00. 





Relative 


Angle of 


amount of 
solar radia- 




tion reach- 




ing earth 


90 


1.00 


70 


0.99 


50 


0.92 


30 


0.75 


20 


0.57 


10 


0.27 


5 


0.07 


. 


. 



It has been found that the longer heat rays are much more 
readily absorbed by the water vapor and carbon dioxide of the 

* Clements, F. E., Research Methods in Ecology, p. 59. 



248 



ELEMENTS OF HYDROLOGY 



earth's atmosphere than the shorter light rays. The light rays 
at the red end of the spectrum are most useful to the plants. 
William Siemens found, in London in 1879 to 1881, while experi- 
menting on the growth of Mimosa pudica,- that the red rays are 
about four times as effective in promoting growth as the white 
rays and ten times as effective as the blue. 



S" 7 
P 

















- Minnesota 






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DURATION OF DAYLIGHT 

IN 

LATITUDE OF STATES 

OF 

Minnesota, Missouri and Mississippi 







































































J J A 

Months 



Fig. 168. 

The amount of daylight during the growing season greatly 
affects the growth of plants. The duration of daylight in vari- 
ous latitudes is shown in Fig. 168. It will be noted that in mid- 
summer, Minnesota has about one and one half hours more of 
daylight each day than Mississippi, besides having a great deal 
more of twilight. 

As transpiration is dependent upon sunlight, shade naturally 
reduces transpiration. Most experimenters have found that 



TRANSPIRATION 249 

complete shading reduces transpiration to about one half or one 
third of that in full sunlight. Hasselbring, experimenting on 
tobacco plants in Cuba, found that the shade of ordinary cheese- 
cloth reduced the transpiration 30 per cent. 

Effect of Soil Moisture. — Most students of the subject of 
transpiration seem to be agreed that the quantity of water used 
by plants during the growing season depends mainly on the 
quantity available within reach of the root system. It has been 
found that, in any given soil, all forms of vegetation wilt when 
the moisture content is reduced to a certain percentage. This 
percentage, however, — known as the " wilting coefficient " — 
varies greatly for different soils. 

The moisture in the soil may, for practical purposes, be 
divided into two portions, namely, "gravity water" or that 
portion which will be drawn down into the lower layers of the 
soil by gravity, and " capillary water " or that portion which 
is held in place in the soil at an elevation of about 5 feet or more 
above the water-table by capillary attraction. Of the capillary 
water, nearly one half is available for plant growth and about 
three fourths will readily evaporate. Of the remainder, — hygro- 
scopic water — little will evaporate from the soil below the upper 
few inches in fields, although it may all be readily driven off by 
heating the soil to a little above 212° F. The relation between 
character of soil and the amount of capillary water, gravity water, 
and hygroscopic water which soil may contain is graphically 
shown in Fig. 169 (a and b). 

Fig. 169 (a) is based upon data taken from the Bulletins of the 
Bureau of Plant Industry, U. S. Department of Agriculture. 
The moisture-holding capacity of a soil is defined as the percent- 
age of water held in short soil columns one centimeter in height. 
The moisture equivalent of a soil is the percentage of water which 
it can retain in opposition to a centrifugal force 1000 times that of 
gravity. The wilting coefficient is the percentage of Abater re- 
tained in soils when plants growing therein wilt to such an extent 
as not to recover turgidity upon being placed in saturated air. 



250 



ELEMENTS OF HYDROLOGY 



The hygroscopic coefficient represents the percentage of water 
which soil contains when kept in a saturated atmosphere. 

The investigations of Briggs and Shantz * indicate that sand 
can, by capillary attraction, hold an amount of water equal to 




Sand 



Loam 



Heavy Dakota Clay 



Fig. 169(a). 



about 2 per cent of its weight. Silt can hold an amount equal 

to about 25 per cent of its weight and clay in highly powdered 

condition can hold an amount of water equal to 100 per cent of 

its dry weight. 

The following table gives the standard classification of soil 

grains adopted by the U. S. Department of Agriculture. 

* Briggs, Lyman J., and Shantz, H. L., Bui. 230, Bureau of Plant Industry, 
U. S, Department of Agriculture. 



TRANSPIRATION 



251 



TABLE 30. — CLASSIFICATION OF SOIL GRAINS 



Fine gravel 
Coarse sand . . . 
Medium sand. . 

Fine sand 

Very fine sand. 

Silt 

Clay 



Name 



Di 


ameter of grain, 




millimeters 


2 


to 1.0 


1 


to 0.5 


0.5 


to 0.25 


0.25 


to 0.10 


0.10 


to 0.05 


0.05 


to 0.005 


0.005 toO 



All particles held on a No. 200 sieve must evidently be classed as sand. 




Sand 



Silt 
MINERAL SOILS 



Clay 



Rich 

Sandy Gumbo Peat 
Loam 
VEGETABLE SOILS 



Fig. 169(b). 



252 ELEMENTS OF HYDROLOGY 

Fig. 169 (b) is based primarily upon the author's studies of soils 
as they occur in the field. The moisture content is expressed in 
inches of water per foot depth of soil under field conditions. 

The moisture available for plant growth in different soils 
under field conditions can be determined, approximately, by 
allowing .4 inch, per foot depth, for sand, 1.0 inch for silt, 
and 1.7 inches for clay, and taking a percentage of these quan- 
tities corresponding to the percentage of particles of the given 
size found in each foot depth of soil under field conditions. 

The effect of vegetable matter is to greatly increase the capil- 
lary water and also, to some extent, the amount of gravity water 
which soils can hold. 

Scientists in various fields have repeatedly stated that it is 
impracticable to express soil moisture in inches of water per foot 
depth of soil under field conditions. The author admits that from 
a laboratory viewpoint and under standardized laboratory methods, 
the determination of soil moisture in terms of the dry weight of 
the soil is the most exact measure available, but he contends that 
this measure affords no satisfactory indication of the relative 
moisture-holding capacities of various soils under field conditions. 
This contention is more forcibly presented by Fig. 169 (a and b) 
than by any arguments which can be made. 

In determining the moisture-holding properties of different 
soils under field conditions the author has adopted the following 
method: A clod of undisturbed soil about the size of a man's fist 
is carefully dug up in the field and all loose particles are removed. 
Most moist soils will retain their shape very well, but where a 
tendency to crumble is manifested, thin, moist tissue-paper or a 
small piece of veil will offer the necessary support. The clod of 
soil is then immediately weighed and its volume determined by 
placing it in a container of known volume and filling all the re- 
maining space with small shot. This virtually amounts to deter- 
mining the specific gravity of the moist field soil by immersion in 
shot instead of water. Later, and at the observer's convenience, 
the dry weight of the material composing the clod of soil is deter- 



TRANSPIRATION 253 

mined by first vaporizing all of the moisture present and then 
weighing the material. These observations give the dry weight 
of a foot of soil under field conditions and also the moisture con- 
tained in a foot of soil in its given condition in the field. This 
field-moisture content, of course, may be more or less than that 
which the soil can hold by capillarity, depending upon the 
depth to the water-table and the climatic conditions which pre- 
ceded the taking of the soil sample. 

A representative sample of the dry soil is next selected and its 
specific gravity determined by immersion in water, by any stand- 
ard method. From the specific gravity and the dry weight of a 
cubic foot of soil under field conditions the voids can be determined, 
and in this way the saturation water-content of the given soil 
under field conditions can be found. 

The specific gravity of most mineral soils varies from 2.65 to 2.69. 
Thepresenceof vegetable matter rapidly reduces the specific gravity. 

In testing for the amount of moisture which various soils can 
hold by capillarity the author first used soil columns 8 to 20 feet 
high and from 2 to 5 inches in diameter. It was found that the 
height of the soil column, when this was more than about 5 feet, 
had no influence on the moisture held by capillarity. It also 
appeared from tests of widely different soils placed in 1 foot layers 
on top of each other, in tubes, that the capillary water held by 
soils was a function of the character of the soil and not of the 
absolute amount of water held in the adjoining soil layers except 
in so far as a fine-grained soil lying on a coarse-grained soil would 
lose its gravity water very slowly. In view of these facts, tests for 
capillary moisture were next made by placing the soil sample on 
top of a permanent test column of very fine sand about six feet 
high. Clods of undisturbed soil, similar to those used in the 
volume determinations, were placed on top of the test column 
whose lower end was kept in water. The soil sample was then 
covered with very fine, wet sand, and then a little additional water 
was added. A water-sealed cover was then placed over the test 
column and after the excess water had drained down through the 



254 ELEMENTS OF HYDROLOGY 

sand column the soil sample was carefully removed, "pared" and 
the water-content determined. 

The rate at which the excess water is drained from the sample 
depends mainly upon its texture. In most cases the water loss 
which occurs between five and twenty days after placing the 
sample is small and inconsequential from a hydrological viewpoint. 
The finer the material constituting the test column, the greater 
the capillary pull and the sooner the excess gravity water is drawn 
down. Knowing the capillary water held by a given soil and its 
saturation water-Content, the amount of gravity water which that 
soil can hold is also known, in practical terms, namely, inches of 
water per foot depth of soil under field conditions. 

Effect of Character of Vegetation. — Even though all plants 
have been found to wilt when the moisture content for a given 
soil has been reduced to a certain percentage, the fact must not 
be lost sight of that in most fields the character of the soil varies 
greatly from foot to foot of depth, and that the roots of dif- 
ferent forms of vegetation penetrate to widely different depths, 
usually adapting themselves, in a measure, to the available 
moisture content of the various soil layers. Frequent light 
sprinkling of lawns is well known to make the grass non- 
drought-resistant, because it coaxes the root system to the 
surface where the greatest supply of moisture is temporarily 
found. Typical root systems of plants are shown in Fig. 170. 

On the whole, the transpiration of deep-rooted vegetation 
will be less fluctuating with changes in monthly rainfall than 
that of shallow-rooted vegetation, on account of the deeper 
layer of soil from which the necessary moisture is drawn. In 
dry seasons deep-rooted vegetation will draw heavily on ground 
storage. The transpiration of shallow-rooted plants growing in 
sandy soils will vary more with rainfall than that of similar 
plants growing in clayey soils. When winter and spring pre- 
cipitation is normally ample to more than supply the full 
requirement of capillary water for the entire depth of soil occu- 
pied by the root system, the transpiration of all plants growing 



TRANSPIRATION 



255 




Oats 



Peach Tree 




Western Grasses 

(a) Sand-grass; (b) sand-sage; (c) bunch-grass; (d) big bluestem; (e) bush 

morning-glory; (f) wire-grass; (g) black grama or short grass. 

Fig. 170. — Typical Root Systems of Plants. 



256 ELEMENTS OF HYDROLOGY 

in sandy soils will vary more with the summer rainfall than that 
of similar plants growing in clayey soils. 

Effect of Precipitation. — The character of vegetation is 
largely determined by precipitation and soil characteristics, 
hence, natural vegetation is a valuable index to both precipi- 
tation and character of soil. 

On the loam soil of eastern Colorado, for example, a short- 
grass cover indicates 15 to 18 inches of annual precipitation. 
The root system of the grasses belonging to this association is 
well developed, but is limited to the upper foot of soil in which 
most of the moisture is found. 

On the loam soil of west-central Kansas, with a rainfall of 
22 to 24 inches per year, wire-grass is found. This grass grows 
taller than short-grass and extends its roots to a depth of about 
3 feet, because the available moisture is found in the upper 
3 feet of soil. Evidently, the increase of 6 to 7 inches in annual 
precipitation over western Kansas, as compared with eastern 
Colorado, has resulted in increased percolation. 

On the loam soil of eastern Kansas, with a rainfall of 26 to 
30 inches per year, bunch-grass, having roots extending about 
five feet down into the soil, is found. Still farther east, in the 
same latitude and under approximately the same conditions of 
temperature and rate of evaporation, where the rainfall is 35 
inches or over and a well-defined water-table is found, forest 
growths predominate. 

For similar conditions of temperature and 15 to 20 inches an- 
nual precipitation occurring largely during the summer months, 
a heavy soil will support only shallow-rooted vegetation, whereas 
a light soil will support deep-rooted plants. 

It will be noted from Fig. 169 (b) that when a heavy soil has lost 
most of its available moisture, an inch of rain, even if it were all 
absorbed, would be held in the upper 6 or 8 inches of soil, whereas 
the same rainfall, if absorbed by a light soil, would penetrate the 
upper 2 feet of soil. As the heavy soil absorbs rainfall much more 
slowly than light soil, resulting in surface runoff, the depth to 



TRANSPIRATION 257 

which a given rain penetrates in a light soil will considerably 
exceed four times the depth of penetration in a heavy soil. 

In connection with the distribution of natural vegetation as 
the result of differences in precipitation and character of soil, 
it is necessary to consider, also, the effects of evaporation. The 
higher the temperature and the lower the relative humidity, 
the greater the rate of evaporation and, consequently, the more 
rain required to grow any given plant on any given soil. For 
example, under practically uniform soil conditions, short-grass 
is found in northern Texas where the annual rainfall is about 
21 inches, in eastern Colorado where it is about 17 inches, and 
in Montana where the annual rainfall is about 14 inches. The 
increased rainfall required in Texas to support short-grass on a 
given soil represents substantially the difference in the rate of 
evaporation between Texas and Montana. 

The short-grass region is limited on the western slope of the 
Rocky Mountains by drought, and in central Texas, Nebraska, 
and Dakota by the deeper-rooted prairie grasses that kill out 
the short-grass by competition. Most of the eastern portion 
of the Great Plains was originally covered with prairie grasses 
which, in turn, gave way in the regions of higher precipitation, 
to forests. The region occupied, in a state of nature, by for- 
ests, almost invariably receives sufficient rainfall and has a soil 
that permits of sufficient percolation to form a well-defined 
water-table. Streams in such a region are, at least in consider- 
able part, supplied by seepage flow. Regions occupied by 
natural upland grasses usually have no well-defined water- 
table except at depths far below the level of the streams. In 
such regions, the minor water courses are dry except after 
heavy rains and the larger streams not uncommonly lose water 
until, in some cases, they disappear entirely. Their ability to 
maintain an existence depends, primarily, upon the degree of 
imperviousness of their beds and banks. 

Transpiration Proportional to Dry Matter Produced. — Most 
experimenters have found that the quantity of water transpired 



258 ELEMENTS OF HYDROLOGY 

by plants varies, approximately, as the quantity of dry sub- 
stance produced. Whether or not this relationship is purely 
accidental does not invalidate the fact. In the 1903 Yearbook 
of the U. S. Department of Agriculture, is given the average 
yield of corn, for 15 years, in the principal corn-growing states, 
together with the average precipitation over those states during 
June, July, and August. When platted, these data indicate an 
average yield of 5 bushels, plus 2 bushels for every inch of rain- 
fall during June, July, and August, between the limits of yields 
of 15 and 35 bushels per acre. 

The data on water requirements of crops, recorded in Bul- 
letin 177, Office of Experiment Stations, and Bulletins 130, 188, 
and 201, Bureau of Plant Industry, U. S. Department of Agri- 
culture, though not conclusive, indicate that the yield of grain 
is approximately proportional to the quantity of water con- 
sumed. Soil evaporation and transpiration are not fully dif- 
ferentiated, however, in most of these experiments. 

Livingston * gives considerable experimental data which show 
an almost direct relationship between transpiration and weight 
of vegetable substance produced. 

The ratio of water used to dry substance produced has been 
found to vary with individual plants and with the plant en- 
vironment. Conifers, in particular, have been found to use less 
than deciduous trees; in fact, some experimenters hold that 
they use less than one sixth as much. For grass and grain, the 
ratio of pounds of water used, to pounds of dry substance pro- 
duced, seems to vary from about 300 : 1 to 600 : 1. 

A full review of the literature on the water requirements of 
plants is given by Lyman J. Briggs and H. L. Shantz in Bul- 
letin No. 285, Bureau of Plant Industry, U. S. Department of 
Agriculture. A summary of the most important observational 
data, taken from this Bulletin, on the water requirements of 
various plants, is given in Table 31. 

* Livingston, B. E., Botanical Gazette, Vol. 40, p. 31. 



TRANSPIRATION 



259 



TABLE 31. — SUMMARY OF WATER REQUIREMENTS OF 
VARIOUS PLANTS (Briggs and Shantz) 



Crop 


Lawes, 1850, 

Rothamsted, 

England 


CO 

>, a P 
i ° 


6 

o & a 

mSoO 


King, 1892 

to 1895, 

Madison, Wis. 


Von Seel- 
horst, 1896 to 
1898, Gottin- 
gen, Germany 


Widtsoe, 

1909, Logan, 

Utah 


5 
"-"—•^ 

lis 

(In 


ceo 
.Sfao 


Wheat 

Oats 


235 


665 

774 


359 
401 
297 
377 


541 
388 

350 


333 


546 


554 

469 
468 


507 
614 


Barlev 


258 


365 
386 




539 


Rye 


724 


Corn 




233 


386 


337 
437 


369 


Sorghum 




306 


Millet 




447 










275 




214 
235 
251 














Peas 


416 


292 


477 

481 




843 


563 


800 


Clover (red) 


330 




Clover (sweet) 












709 


Alfalfa 
















1068 


Horse beans 






263 
373 












Lupine 




























818 




Buckwheat 




. .646 


371 
337 








578 


Rape 




912 
843 
490 










441 


Mustard 










496 




Sunflower 














Potatoes 






423 


281 






448 


Linseed. . 










807 
263 
312 
635 
598 
811 
212 




Eleusine. . . 
















Paspalum 
















Cajanna 
















Cyamopsis 




i 










Rice 














Sugar cane j 












Sugar beets 










497 


377 


Salsola 










336 


Amaranthus 














303 


Artemisia '. . | 














765 


j 

















In view of the substantially constant relationship, as found 
by most experimenters, between transpiration and vegetable 
substance produced by any given species of plant, yields of hay, 
grain, etc., become a convenient index to the approximate, 
relative quantities of transpiration to be expected on different 
watersheds, and on the same watershed in different years. 

Amount of Transpiration in Inches Depth over Ground Area. 
— No more uncertain factor enters into computation of rainfall 
losses than the amount of water used by growing plants. Most 
of the available data are inapplicable to the problem or so 



260 ELEMENTS OF HYDROLOGY 

widely divergent as to be of little value. Laboratory results 
are usually based on experiments with single plants, with no 
indication of the ground space covered by the plants. The 
time over which the observations extended and relevant mete- 
orological data are usually missing. Frequently, transpiration 
is compared with other phenomena, such as evaporation from 
water or soil surfaces, or precipitation. The divergence of 
opinion with respect to the amount of transpiration is well indi- 
cated by the fact that Schleiden thought the transpiration from 
a forest was three times the evaporation from a water surface 
of equal area, whereas Shiibler thought it only one quarter as 
great. Extreme values given for annual transpiration vary 
from less than 1 inch to 16 feet! Most of the values given for 
forest trees and small grains, however, vary from 4 to 9 inches 
per year, with occasional values for oats and some grasses run- 
ning up to 14 and 15 inches per year.* If plants, under field 
conditions, transpired a quantity of water equal to from one 
half to two times the evaporation from an equivalent surface of 
water, as claimed by some experimenters, a great many streams 
in the United States that have a very appreciable, sustained 
flow would become intermittent, because there would be no 
ground-water supply to feed them. Surface runoff alone would 
appear in these streams. 

* The experimental determinations of the transpiration of various plants, 
as given by Risler, Hohnel, Shiibler, Hales, Hartig, Hellriegel, Sachs, Wollny, 
and others, are so divergent that the author felt it was of questionable utility 
to present these results here, except as briefly summarized above. 

In most instances, only abstracts of the published results of these investi- 
gators were available to the author. These abstracts were so lacking in 
essential, related, meteorological phenomena as to make the transpiration 
determinations of relatively little value for present purposes. Frequently, 
daily transpiration would be stated, without reference to length of growing 
season, hours of sunshine, temperature, humidity, etc. 

In published abstracts of the investigations above referred to, deductions, 
as to water consumption of plants, have frequently been made based on 
some assumed length of season, and the like. Where experimental data 
were given for single trees, for example, a certain number of trees were as- 
sumed per acre, for the purpose of deducing a value of transpiration in 
inches depth on the ground area. 



TRANSPIRATION 



261 



In estimating the transpiration loss from a watershed, the 
exact character of the vegetation is not as important a factor 
as it might at first appear. Except for unoccupied lands in the 
arid and semi-arid region, hardly a watershed of considerable 
size can be found that is given over purely to one class of vege- 
tation. Practically all watersheds are covered with mixed 
vegetation, including trees, shrubs, grasses, or grains. Cut- 
over watersheds quickly grow up to grasses, weeds, and herbs 




Fig. 171. — Rocky, Burnt-over Watershed thoroughly covered with 

Vegetation. 



of various kinds, which in turn are soon supplanted by shrub- 
bery, brush, and then a growth of young trees. Areas of agri- 
cultural land not under cultivation, or after harvest and before 
fall plowing, soon become thoroughly covered with self-sown 
grain, weeds, and grasses, and hence suffer a transpiration loss 
perhaps fully as high as though they were producing crops. 
Even the rugged watersheds of mountain ranges, below the 
timber line, are usually well covered with brush, grasses, moss, 
and other forms of low-growing vegetation. Burnt-over water- 
sheds with scanty covering of soil, and rock outcropping every- 
where, as in the northeastern part of Minnesota, are also well 



262 ELEMENTS OF HYDROLOGY 

covered with vegetation of one kind or another, as is shown in 
Fig. 171. As a consequence, the normal transpiration loss, so 
far as it is determined by the character of vegetation on 
different watersheds, does not vary between wide limits. 

For tentative purposes, the following normal seasonal tran- 
spiration may be used as a base value in estimating water losses 
for the north central portion of the United States: 

9 to 10 inches for grains, grasses and agricultural crops; 

8 to 12 inches for deciduous trees; 

6 to 8 inches for small trees and brush; 

4 to 6 inches for coniferous trees. 

These quantities represent inches depth of water over the 
entire area occupied by the given form of vegetation. The 
monthly distribution of this total seasonal transpiration is de- 
termined mainly by the monthly mean air temperature as 
given in Fig. 164, page 244. These base values of monthly 
transpiration must then be modified for deficient or excess 
precipitation and ground-water supply in the soil occupied by 
the root system of the given form of vegetation, to ascertain 
the probable monthly transpiration under the given conditions. 



CHAPTER VIII 
DEEP SEEPAGE 

The Underground Reservoir. — The presence of artesian 
water supplies over large areas in the United States is conclusive 
proof that some precipitation seeps down through the upper 
layers of soil and subsoil into the underlying rock strata. The 
percolating water flows along through these porous strata until 
they have dipped down below impervious strata and entrapped 
the water in underground reservoirs, from which it may again 
be drawn by deep wells, or from which it may eventually flow 
to the sea. 

The term deep seepage, as here used, does not include the 
percolating precipitation which moves through the drift cover- 
ing the rock strata and furnishes the seepage flow of streams. 
The actual amount of deep seepage can never be accurately 
determined, yet when we consider the fact that the entire 
domestic water consumption is equivalent to only about 
.1 inch of rainfall per annum and that only a relatively few 
artesian sources of supply are in use and that such supplies have 
frequently been found to become reduced and even exhausted 
after a relatively few years' draft, it becomes apparent that 
the aggregate amount of deep seepage, in so far as abstractions 
or additions to the flow of streams is concerned, must usually 
be inconsequential. # 

It is not intended to convey the impression, however, that 

the total amount of underground water, extending down to 

the depth of about six miles, according to Van Hise,* at which 

the pressure of the overlying weight of rock becomes so great 

as to reduce the porosity to zero, does not aggregate a tremen- 

* Van Hise, C. R., 16th Annual Report, U. S. G. S., Part 1, 1896, p. 593. 

263 



264 ELEMENTS OF HYDROLOGY 

dously large quantity. Most of this great reservoir of under- 
ground water, however, calculated by Slichter * as amounting 
to about 565 million, million cubic yards, must always remain 
unavailable for direct use by mankind. 

The available artesian water supply is determined by the 
area over which the pervious stratum, interspersed between 
two layers of impervious strata, outcrops, the amount of rainfall 
which percolates deeply into this outcropping stratum, and 
the rate at which the underground water can flow through 
the porous stratum toward the wells from which it is drawn. 

While none of the rock strata, except when under tremendous 
pressure, can be considered as entirely impervious, granitic 
rocks usually contain less than 1 per cent of voids, limestone, 
from 1 to 5 per cent, while sandstones contain from 6 or 7 
per cent, to more than 25 per cent of voids. Although the 
voids in clay are relatively large, the pore spaces are so small 
that most of the water is held by capillarity and that which can 
be drawn by gravity moves so slowly as to make clay strata 
relatively impervious. 

Artesian waters are usually hard and often quite warm. 
Temperatures of 80 to 90 degrees are not uncommon in the 
Dakota basin. 

Artesian Basins. — The principal artesian supplies in the 
United States are derived from the Potsdam and the St. Peter 
sandstone. The former lies between the impervious Archean 
rocks and the lower magnesian limestone, and the latter 
between the lower magnesian and the Trenton limestones. 
About 12,000 square miles of Potsdam outcrops and about 
3000 square miles of St. Peter outcrops occur in central Wis- 
consin and eastern Minnesota. These sandstone strata have 
a slope toward the south and soon dip below the impervious 
limestone, creating the best artesian well region in the United 
States, in southern Wisconsin and Minnesota, throughout 

* Slichter, C. S., The Motions of Underground Waters, U. S. G. S. Water 
Supply Paper No. 67. 



DEEP SEEPAGE 



265 



Iowa, most of Illinois, northwestern Indiana and northern 
Missouri. 




Fig. 172. — Outcrops of Potsdam and St. Peter Sandstones. 
(Figures indicate elevation above sea-level.) 

The Potsdam and St. Peter outcrops are shown in ,Fig. 172 
and a section throughout this basin, based on a paper by Mead,* 
is shown in Fig. 173. 



* Mead, D. W., The Hydro-geology of the Upper Mississippi River Basin, 
Jour. Assoc. Eng. Soc, 1894, p. 396. 



266 



ELEMENTS OF HYDROLOGY 




-Jj>7^ LevelXake MiJjhig-an_- 

Archean Rocks 






' i/' 






From a Paper by Daniel W. Mead, Jour. Assoc. Eng. Soc., 1894, p. 396. 

Fig. 173. — General Arrangement of Water-bearing Sandstones. 

(Section through southern Wisconsin and northern Illinois. Greatly enlarged vertical scale. ) 

As most of the outcropping sandstone is now covered deeply 
with glacial drift, usually containing thick layers of clay, the 
percolation of rain-water into these pervious sandstone layers 
is necessarily very slow. In fact, the existence of many small 
lakes and ponds seems to be possible only because the under- 
lying clay is almost impervious. In most cases, percolation, 
however, is no doubt more than able to supply water more 
rapidly than the porous strata can conduct it away. 

Numerous artesian wells in the upper Mississippi basin have 
been driven to considerable depths, through the overlying drift, 
limestone and sandstone layers, and over 1000 feet into the 
Potsdam sandstone. This brings the bottom of the well far 
below the level of the sea. 

Other large and important artesian well regions are those 
in Dakota, Texas, California and on the eastern slope of the 
Appalachian Mountains. Minor basins are found throughout 
the Rocky Mountain region. The Dakota wells are relatively 
deep and are noted for their high pressure. The water-bearing 
stratum is the Dakota sandstone of the cretaceous period, 



DEEP SEEPAGE 



267 



ui,->]i;g I 






u. 



uircjjaqtuuqo 




uaajn »uu3llsxio 



f * 
S H 



s " 



X 



5 J3 -^ 



03 sa 



3 - 



« 2 2 

d ? *> 

.S Ml 

J5 O St 



& a 



&« 



268 ELEMENTS OF HYDROLOGY 

outcropping on the eastern slope of the Rocky Mountains 
at an elevation of about 3000 feet above sea-level. A section 
through the Dakota artesian basin is shown in Fig. 174. 

The Potsdam and the St. Peter sandstone strata, the former 
increasing rapidly in thickness toward the south, have a gentle 
slope toward the sea, and no doubt some of the deep seepage 
finds its way directly into the ocean through these strata. 

Artesian supplies in the Gulf and South Atlantic Coast region 
are derived mainly from sand and gravel deposits underlying 
a hard blue clay. The waters are soft and very satisfactory 
for domestic purposes. 

Great fresh water springs occur ten to fifteen miles out in the 
ocean from the Florida, Gulf shore at depths of 100 to 300 feet. 

In 1886, wells in Pensacola, Fla., from 60 to 280 feet deep and 
one and one-half miles from shore, rose and fell 6 to 10 inches 
daily, " apparently with the tide." 

Motion of Underground Water. — Ground water, flowing 
through the capillary interstices of the soil and the rock, moves 
very slowly. Even in relatively coarse sands, the rate of motion 
is only a mile or two a year. In gravel, the flow may reach 
several miles a year, depending largely upon the pressure head 
and the character of the material. Evidently, then, it would 
take water percolating into the Potsdam outcrop in Wisconsin, 
a great many years, possibly one or two thousand, to reach 
the Gulf of Mexico. 

Some measured rates of underflow through superficial deposits 
are one-fifth to three-quarter mile per year in the Arkansas 
River basin, one-half to four miles per year in the Mohave 
River basin, one and one-fifth miles per year in the Republican 
River basin in Kansas, and about one-third mile per year on 
Long Island. 

Poiseuille, in 1842, concluded, from experimental obser- 
vations, that the flow of fluids through capillary interstices 
varied directly as the pressure. This was later verified for air 
by Meyer, and for water by Darcy, who in 1856 set forth the 



DEEP SEEPAGE 269 

relation between the velocity of flow, character of soil, pressure 
head and length of soil column in the following formula: 

v = k r 

in which 

v = the velocity of the moving ground water; 

h = the difference in pressure-head; 

I = the length of the soil column; 

k = a coefficient depending upon the character of the soil, 
especially upon the size of the soil grains. The size 
of soil grain was to be determined experimentally 
by Darcy's apparatus. 

Hazen Formula. — In 1892 Hazen * produced the formula: 

v = cd 2 j (0.70 + 0.03 1), 
in which 

v = the velocity of water in meters per day through the 

entire cross-sectional area; 
t = temperature of water in °C; 
h — head acting on water; 
I = length of soil column; 

d = " effective size " of soil grains in millimeters; 
c = a constant varying from 400 to 1000. 

Hazen defined "effective size" as such a size that 10 per cent 
of the material is of smaller grains and 90 per cent of larger 
grains. Hazen found that the 10 per cent of small-size grains 
virtually determined the capacity of sands to transmit water. 

In addition to using the term "effective size" in differentiat- 
ing the sands tested by him, Hazen used the term "uniformity 
coefficient." This represents the ratio of the size of grain, which 
has 60 per cent of the sample finer than itself, to the effective 
size. Hazen indicated in his Report, that on the basis of the 
data from which his formula was derived, its application could 

* Hazen, Allen, Report Mass. State Board of Health, 1892,. p. .541.,.. 



270 



ELEMENTS OF HYDROLOGY 



OvarflowX 



MMMSm 



; Loss of 
I Head 



only be justified for sands having a uniformity coefficient below 
5 and an effective size of between .1 and 3 millimeters. He 
also remarked that sharp-grained material with uniformity 
coefficients below 2 would have nearly 45 per cent of open space, 
or porosity, as ordinarily packed, and sands having coefficients 
below 3, as they occur in the banks or artificially settled in water, 
would usually have 40 per cent porosity; with more mixed 

materials, the closeness of 
packing increases so that 
with a uniformity coefficient 
of 6 to 8, only about 30 per 
cent porosity would be ob- 
tained. In general, round- 
grained water-worn sands, 
according to Hazen, would 
give from 2 to 5 per cent 
less porosity than sharp- 
grained sands. 

The apparatus used by 
Hazen in determining his 
law for the flow of water 
through sand is shown in Fig. 175 and the results obtained 
with the sand tested, which, according to Hazen's comment 
above noted, probably had a porosity of about 40 per cent, are 
given in Table 32. The values have been reduced from meters 
per day to feet per day. 

The relative flow through the same sand for different water 
temperatures as determined by Hazen is given in Table 33. 

Hazen found that for gravels of an effective size of about 
3 millimeters, the general formula was not exactly applicable, 
as the velocity no longer increases as rapidly as the square of 
the effective size. Coarse gravels, also, indicate a velocity 
varying as the square root of the head, instead of the first power 
of the head, as in the case of sands. The effect of temperature 
also becomes less marked in the case of gravels. 



Fig. 175. — Hazen's Apparatus for Deter- 
mining Flow of Water through Sand. 



DEEP SEEPAGE 



271 



TABLE 32. — FLOW OF WATER THROUGH SAND (Hazen) 

Temperature = 50° F. 

Uniformity coefficient less than 5 (apparently about 2.5) 

Porosity, about 40% 

Gradient y = 1 





Effective size in millimeters 




0.10 


0.20 


0.30 


0.40 


0.50 


1.00 


3.00 


Discharge * 

Velocity t • 


33 

82 


131 

328 


295 

738 


525 
1312 


820 
2050 


3280 
8200 


29,500 
73,800 



* Discharge in cubic feet per day per square foot of gross cross-sectional area. 

t Velocity (assuming 40 per cent porosity) in feet per day through actual pore space. 



TABLE 33. — EFFECT OF TEMPERATURE ON FLOW OF 
WATER THROUGH SAND (Hazen) 



Temperature, degrees F. . 

Relative velocity and 
discharge 



32 c 



0.70 



41' 



0.85 



50° 
1.00 



59° 
1.15 



68° 
1.30 



77° 
1.45 



86° 
1.60 



Table 34 gives Hazen's results for coarse gravels of relatively 
uniform size, i.e., having uniformity coefficients varying from 
1.4 to 2. 



TABLE 34. — FLOW OF WATER THROUGH GRAVEL (Hazen) 

Temperature = 50° F. 

Uniformity coefficient 1.4 to 2.0 

Porosity = about 45% 



h 


Discharge in cubic feet per day through gross cross-sectional area for 
given effective size of grain in millimeters 


I 


3 mm. 


5 mm. 


10 mm. 


20 mm. 


30 mm. 


40 mm. 


0.0005 

0.0010 

0.002 

0.004 

0.006 

0.008 

0.010 

0.015 

0.020 

0.030 

0.050 

0.10 


11.5 

23.0 

46.0 

88.5 

134.5 

177.0 

220.0 

322.0 

416.0 

606.0 

918.0 

1625.0 


32.8 

68.9 

131.0 

252.0 

367.0 

465.0 

567.0 

780.0 

984.0 

1310.0 

1836.0 

3050.0 


98.4 

190.0 

361.0 

682.0 

902.0 

1115.0 

1262.0 

1575.0 

1902.0 

2460.0 

3480.0 

5080.0 


262 

485 
902 
1575 
2035 
2360 
2720 
3380 
3870 
4750 


492 
902 
1575 
2430 
3050 
3580 
4000 
4850 


820 
1476 
2330 
3280 
4060 
4750 



272 ELEMENTS OF HYDROLOGY 

Slichter's Formula. — Slichter,* on the basis of a theoretical 
investigation, verified, however, by a long series of carefully 
conducted experiments by King,f determined the following 
equation for the flow of water through sand: 

hd 2 s 
q — 0.2012 —p^ cubic feet per minute, 

where 

h = head acting on water; 
s = cross-sectional area of soil column; 
I = length of soil column; 
d = mean size of soil grains in millimeters; 
u = a coefficient depending upon the temperature; 
K — a coefficient depending upon the porosity of the soil. 

Slichter defined " mean " or " effective size " as such a size 
" that if all the grains were of that diameter, the soil would have 
the same transmission capacity that it actually has." 

When the cross-sectional area term is omitted, Slichter's 
formula also reduces to the original Darcy formula, namely: 

v = k j with k, however, a variable. 

Poiseuille, Meyer, Darcy, Hazen, and Slichter all agreed that 
the flow of water through capillary interstices varies directly 
as the pressure-head and inversely as the length of the soil 
column. King J found a slight tendency for flow to increase 
somewhat faster than pressure. 

Darcy's formula took account only of pressure-head and length 
of soil column. Hazen added the effect of temperature and 
size of soil grain, stating an approximate value for porosity. 
Slichter's formula includes not only pressure-head, length of 
soil column, effective size of soil grain, and temperature of water, 
but a great range of porosity. 

* Slichter, C. S., 19th Annual Report U. S. G. S., Part II, 1899, p. 295. 
The Motions of Underground Water, U. S. Water Supply Paper No. 67. 
t King, F. H., 19th Annual Report U. S. G. S., Part II, 1899. 
\ King, F. H., 19th Annual Report U. S. G. S., Part II, 1899, p. 59. 



DEEP SEEPAGE 



273 



Table 35 gives the effect of temperature on the flow of water 
through sand columns as given by Slichter. 

TABLE 35. — EFFECT OF TEMPERATURE ON FLOW OF 
WATER THROUGH SAND (Slichter) 



Temperature, de- 
grees F 



Relative velocity 
and discharge . . . 



32° 


40° 


50° 


60° 


70° 


80° 


90° 


0.74 


0.85 


1.00 


1.16 


1.34 


1.51 


1.70 



100° 
1.90 



Table 36 gives the transmission constant k or the discharge 
in cubic feet per day, through a soil column 1 foot long, under a 
head of 1 foot of water. 



TABLE 36. — FLOW OF WATER THROUGH SAND (Slichter) 

Temperature = 50° 

Porosity = 40% 

Gradient 7=1 



Diameter (mm.) . . 

Discharge * 

Velocity f 



Silt 



0.01 
0.11 

0.28 



0.02 
0.43 
1.07 



Very fine sand 



0.04 
1.74 
4.35 



0.06 
3.92 
9.80 



0.08 

6.95 

17.35 



Fine sand 



0.10 
10.9 
27.3 



0.15 
24.4 
61.5 



0.20 
43.5 
109.1 



Diameter (mm.) 
Discharge * . . . . 
Velocity f 



Medium sand 



0.30 
98.0 
244.0 



0.40 
174.0 
435.0 



Coarse sand 



0.50 
272.0 
680.0 



0.60 
393.0 
983.0 



0.75 

610.0 

1530.0 



Fine gravel 



0.90 
880.0 
2200.0 



1.00 
1088 
2720 



3.00 

9,770 

24,400 



5.00 
27,100 
67,800 



* Discharge in cubic feet per day per square foot of gross cross-sectional area. 
t Velocity in feet per day through actual pore space. 

The effect of porosity on the flow of water through sand as 
given by Slichter is shown in Table 37. The effect of porosity 
as given in this table represents the effect of packing the same 
sized grains in different ways. 

TABLE 37. — EFFECT OF POROSITY ON FLOW OF WATER 
THROUGH SAND (Slichter) 



Porosity, or per cent 
voids 



Relative discharge . 
Relative velocity 



26 


28 


30 


32 


34 


36 


38 


40 


42 


44 


0.244 


0.306 


0.388 


0.478 


0.584 


704 


0.842 


1.000 


1.172 


1.378 


0.376 


0.437 


517 


0.597 


0.687 


0.781 


0.886 


1.000 


1.118 


1.251 



1.591 
1.385 



274 ELEMENTS OF HYDROLOGY 

Comparison of Formulas of Slichter and Hazen. — A com- 
parison of the results of the investigations of Slichter and Hazen 
indicates that for a given slope and for all effective sizes from 
.1 mm. to 3 mm., Hazen found a discharge almost exactly three 
times as great as that found by Slichter. 

Slichter defined " effective size " * as such a size " that if all 
grains were of that diameter, the soil would have the same 
transmission capacity that it actually has." Hazen defined 
" effective size " as such a size that 10 per cent of the material 
is of smaller grains and 90 per cent of larger grains. Although 
Hazen concluded that the particles which constitute the 
finer 10 per cent of the sample of sand virtually determine its 
transmission capacity, he nevertheless recognized the possible 
effect of the other 90 per cent of the particles, by stating that 
his formula was applicable only to sands having a uniformity 
coefficient less than 5. Apparently, Hazen's formula was based 
mainly on experiments with sands having a uniformity coeffi- 
cient of about 2J, possibly as low as 2. 

Slichter's formula is based on a theoretical analysis, assuming 
uniform-sized, spherical grains. In so far as the formula was 
tested experimentally by King, uniform-sized grains were used. 
Slichter's results, then, assume a uniformity coefficient of 1. 
All natural sands have a uniformity coefficient greater than one. 
An increase in uniformity coefficients means a decrease in poros- 
ity, and, hence, a decrease in transmission capacity. The larger 
the grains for a given porosity, the greater the transmission 
capacity. The effective size of natural sands, then, of given 
transmission capacity must always be greater than the effective 
size of uniform-grained sand of the same transmission capacity. 
In other words, the effective size of Slichter's sand is always 
less than the effective size of Hazen's sand of equal transmission 
capacity. This, however, does not explain the almost exact 
difference of 300 per cent in the results as given by Slichter 
and Hazen for all effective sizes. 

* The Motions of Underground Waters, pp. 22, 27. 



DEEP SEEPAGE 



275 



to 






30 



25 



JO 











' 












RELATION BETWEEN 

UNIFORMITY COEFFICIENT 

AND POROSITY OF SANDS 

Based on Physical Properties of 202 Sands 

Reported in Bulletin No.58 

U.S. Bureau of Standards 

1916 
















































- 



3 4 5 6 

Uniformity Coefficient 

Fig. 176. 




0.8 l.o 1.2 
Size of Opening - mm. 

Fig. 177. 



276 ELEMENTS OF HYDROLOGY 

Fig. 176 based on the physical properties of 202 sands, reported 
in Bulletin No. 58, Bureau of Standards, U. S. Dept. of Commerce, 
June 20, 1916, shows the average relation between the uniform- 
ity coefficient and the porosity of sand. Although individual 
sands show considerable departure from the mean relationship 
here expressed, yet the data at hand show reasonable corre- 
spondence. 

It will be noted that Hazen's general statement, page 270, re- 
garding the effect of uniformity on porosity is in agreement 
with Fig. 176. 

Fig. 177 shows graphically the physical properties of five 
widely different sands conforming to the above expressed relation- 
ship between uniformity coefficient and porosity. 

Measurement of Underflow. — While the formulas previ- 
ously discussed are of value in connection with works for the 
collection and filtration of public water supplies, and serve 
also to give a general comprehension of the movement of under- 
ground water, actual measurements of the velocity of under- 
flow are frequently of great engineering value. The best form 
of apparatus yet devised for this purpose is that invented by 
Professor C. S. Slichter of the University of Wisconsin. 

The essentials of the apparatus are shown in Fig. 178. 

An electrolyte, usually ammonium chloride, or caustic soda, 
is introduced into a well and its movement registered by an 
ammeter placed in an electric circuit running between the 
casings of the wells. An electrode, placed in the lower well 
but insulated from its casing, is joined into the circuit. As 
the electrolyte flows with the ground-water toward the lower 
well, the current registered by the ammeter increases until, 
when the electrolyte reaches the lower well, a sudden rise in 
current due to a short circuit is registered. A typical graph 
of the results obtained in an actual measurement is shown in 
Fig. 179. The time interval between points, which represents 
the instant when the electrolyte was introduced into the upper 
well, and point B (the point of inflection on the curve), which 



DEEP SEEPAGE 



277 




Fig. 178. — Slichter's Apparatus for Determining Flow of Underground 

Water. 




213 4 5 6 7 i 8 9 10 11 12 1 2 3 4 5 6 7 8 
P-M. ! A - i B A.M. 

Time 

Fig. 179. — Curve obtained by Slichter's Method of Determining the Velocity 

of Ground-water. 
(The distance AB represents the time of passage of the ground-water from the upper to the 
lower well. The point B should be taken at the point of inflection of the curve and not at the 
highest of maximum point. If the point of inflection be taken the effect of the diffusion of 
the electrolyte will be nullified. — Slichter.) 



278 ELEMENTS OF HYDROLOGY 

represents the time when it reached the lower well, is the time 
required for the ground-water to move between the two wells. 
Knowing the velocity of flow, the pore spaces must be deter- 
mined or estimated and from these two quantities the discharge 
per unit of cross-sectional area of porous stratum can be de- 
termined. The total amount of underflow, of course, depends 
also upon the total cross-sectional area of porous stratum under 
investigation. 




-OFF 



Prepared by Henry Gannett 
mainly from data of the 
United States Geological Survey 




B ii i/i t. fli 



MAP OF UNITED STATES, SHOWING MEAN ANNUAL RUN-OFF 
Red lines and figures indicate average annual run-off in depth in inches 

Fig. 180. 



Prepared by Hanry Gann- 
mainly Itorr data of tha 
Umtad Slataa Gaotogieal 5ui 



CHAPTER IX 
RUNOFF 

Definition. — Runoff is the technical name applied to that 
portion of the precipitation which is carried off from the land 
area into the ocean through surface channels. It constitutes 
the residual precipitation after evaporation, transpiration, 
and deep seepage losses have been supplied. Being a residual, 
runoff necessarily cannot be a percentage of the rainfall, i.e., 
the runoff must be determined by deducting losses from pre- 
cipitation and not by taking a percentage of the precipitation. 

Speaking in very general terms, the demands of evaporation 
and transpiration require from about 15 to 25 inches of pre- 
cipitation per annum. The remainder represents runoff. Fig. 
180 shows the approximate mean annual runoff in the United 
States, according to the U. S. Geological Survey. 

SURFACE FLOW 

Broadly speaking, runoff consists of surface flow and seepage 
flow. The factors modifying the surface flow will first be dis- 
cussed. These factors may be subdivided into the character and 
'rate of precipitation, and the physical characteristics of the 
watershed. 

Effect of Precipitation and Temperature. — Large surface 
flow is ordinarily produced by heavy precipitation occurring 
in a short interval of time. In northern latitudes considerable 
precipitation may accumulate on the ground as snow, and a 
large portion of this may be suddenly carried into the streams 
by warm rains or high temperatures. In the Ohio Valley, for 
example, the precipitation is quite uniformly distributed through 
the year, amounting to about three to four inches per month. 

279 



280 ELEMENTS OF HYDROLOGY 

Occasionally, a large portion of the winter precipitation falls 
as snow, remaining on the ground until it is carried off into the 
streams by warm spring rains or high temperatures or by a 
combination of the two. 

Over the Northwest, the winter precipitation is relatively light, 
averaging only about 1 inch per month, but the temperatures 
are lower, so that considerable snow may accumulate during 
the winter months. The probabilities of high surface flow 
are less here than in the Ohio Valley, however, notwithstanding 
the winter's accumulation of snow, because the temperature 
rises rapidly in the spring, normally causing the melting of the 
accumulated snow before heavy rainfall sets in. Moreover, 
the ground, in the Northwest, usually freezes up while in a 
comparatively dry state and hence permits considerable per- 
colation, in spring, even while still frozen. 

In the Southwest, no snow accumulates, but the summer 
precipitation is much greater than in the Ohio Valley. High 
surface runoff here results from excessive precipitation over 
restricted areas . 

Effect of Physical Characteristics of Watershed. — Given 
rates of precipitation cause different surface flows from water- 
sheds of varying character and condition. An impervious, 
steeply sloping drainage area may shed substantially all of the 
rain falling upon it. A drainage area may be impervious on 
account of outcropping rocks, frozen and ice-covered ground, 
or saturation. Perhaps the highest degree of imperviousness 
is attained by saturated, frozen ice-covered ground. Substan- 
tially all of the rain falling upon such ground will run off into 
the water courses, occasionally carrying ice or snow with it in 
sufficient quantity to make the runoff exceed the rainfall. When 
sandy soil freezes up after thorough drainage has been permitted, 
it will remain more or less pervious and absorb a surprisingly 
large amount of rain after the ice cover has been removed, but 
before the frost is out of the ground. 

A watershed, impervious on account of outcropping rocks, 



RUNOFF 281 

nevertheless absorbs a moderate amount of water at the begin- 
ning of a rainstorm on account of the moss and humus found 
in the crevices of the rocks. After such storage capacity is 
exhausted, however, substantially all of the succeeding rainfall 
will run off into the water courses and into lakes, ponds, 
marshes and swamps, common to such watersheds. 

When heavy rains continue for some time, all but the most 
sandy and gravelly watersheds become temporarily impervious 
through saturation of the soil. For any given rainfall, the total 
surface runoff from a pervious, sandy watershed will necessarily 
be less than that from other watersheds, by the amount of water 
required for saturation. Sandy watersheds frequently exhibit 
no signs of surface runoff. The presence of gullies is an unmis- 
takable sign of surface runoff. 

In the spring and fall of the year, when evaporation and tran- 
spiration losses are small, all soils, as a rule, carry substantially 
the entire possible amount of capillary water, between rains. 
Under such conditions, the capacity of sand for gravity water 
is about four inches per foot depth, whereas the capacity of 
heavy clay is but a little more than an inch. In consequence, 
clay soils quickly become saturated and permit large surface 
runoff. While clay soils nominally have great moisture hold- 
ing capacity, not only is the rate of absorption of water very 
slow, but under field conditions clay soils hardly ever dry out 
except at the surface, so that their actual capacity for moisture 
is usually very much less than that of sandy soils. 

Land under cultivation will, in the spring and fall, absorb 
considerable rain and thus reduce the surface runoff. All 
vegetation will retard the surface runoff somewhat, but its 
effect is soon lost in case of heavy rains. Virgin forest with 
deep humus cover, though of rare occurrence, has considerable 
absorptive capacity. 

The steeper the slope of a watershed, the greater the sur- 
face runoff, but the effect of ruggedness is not as great as might 
be imagined. Leaving out of consideration very flat watersheds, 



282 ELEMENTS OF HYDROLOGY 

the effect of slope on the total surface runoff is relatively small. 
It affects, primarily, the time within which the surface waters 
reach the various channels. 

Effect of Drainage of Upland. — Comparatively few ob- 
servational data are available respecting the effect of tile and 
open ditch drainage on the flow of streams. The views held 
by engineers regarding the effect of drainage are about as widely 
divergent as those regarding the effect of forests. Much of 
this divergence of opinion appears to be the result of reasoning 
from different premises. 

The effect of drainage, as of forests, is not a single, uniform one. 
Believing that a statement of " effects " should always be coupled 
with a specific statement of the " conditions " under which 
these effects are produced, the author has endeavored, in the fol- 
lowing pages, to deal with one phase of the subject of drainage 
and forests at a time. All but the very smallest watersheds 
are a combination of diverse characteristics; consequently the 
sum total of the effect of drainage and forests upon the flow 
of streams must be based upon an understanding, so far as 
our present knowledge permits, of how these factors influence 
stream flow under specific conditions. 

Both open and tile drains placed in upland fields facilitate 
and hence increase surface runoff, but, on the whole, have an 
equalizing tendency. In so far as tile drains intercept water 
which has already passed beneath the surface of the ground, 
and bring it into open channels again, they must inevitably 
increase the total surface runoff and reduce the seepage flow. 
By maintaining a more open soil texture, and by quickly re- 
ducing the moisture content of the soil above them to that 
which the soil can hold by capillarity, i.e., by removing gravity 
water amounting to from 1| to 4 inches per foot depth of soil, 
tile drains increase the capacity of the soil for absorbing water 
during rains, and thus tend to lengthen the time within which 
a given amount of runoff reaches the water course. In other 
words, tile drains on upland fields usually tend to equalize 



RUNOFF 283 

the surface runoff. During torrential summer rains, however, 
the rate of absorption of water by even the best drained heavy 
clay soils, is altogether too slow to prevent excessive surface 
runoff even from flat slopes. Open ditching, under such con- 
ditions, facilitates rapid surface runoff and increases flood flows. 

Effect of Drainage of Swamps. — The drainage of swamps 
and bogs, particularly those having a heavy covering of peat 
vegetation and the water-table near the surface of the .ground, 
usually has an equalizing effect upon the flow of streams. Peat 
vegetation, and the resulting humus following drainage and 
decay of the vegetable fiber, quickly absorbs large quantities 
of precipitation. As the pore spaces are large, however, such 
soil rather readily delivers up its burden of gravity water to 
the drains below. The temporary storage capacity of such 
vegetable soils, nevertheless, is greatly increased by drainage 
and the total evaporation loss is decreased. As, under the 
conditions assumed, the water-table was above the level of 
tile drains before the drainage system was established, drain- 
age of such soils does not result in intercepting any large 
portion of the percolating water that supplies the seepage flow, 
hence this is not greatly reduced by drainage. Drainage of 
swamps and bogs with peaty soils, then, usually reduces the 
ordinary flood runoff, increases the total runoff, does not mate- 
rially decrease seepage flow; in short, drainage of such soils 
tends to equalize stream flow. 

Effect of Lakes and Ponds. — Ordinary surface runoff, re- 
sulting from moderate rains, is retarded and equalized and, 
to some extent, diminished, by lakes and ponds. All pond 
holes, no matter how small, have some retarding effect" on run- 
off, tending to reduce the rate and extend the period of time 
over which runoff occurs. Ponds, in so far as they are wet- 
weather phenomena, may, to some extent, increase percolation. 
Lakes and other permanent bodies of water usually exist because 
percolation is nil or exceedingly slow. They are, as a rule, 
fed by both ground and surface waters, and, consequently, can- 



284 ELEMENTS OF HYDROLOGY 

not add to the ground-water supply through percolation. All 
permanent bodies of water greatly increase evaporation losses 
from a watershed by providing a continuous supply of moisture, 
and consequently reduce the total available runoff. The greater 
the depth of lakes, however, the lower their temperature and the 
smaller the evaporation loss. 

Marshes and swamps whose beds are sufficiently impervious 
to maintain a supply of- water throughout the year not only 
increase evaporation losses but greatly increase transpiration 
losses by sustaining a luxuriant growth of grasses or timber. 
Swamps and marshes, while tending to retard and equalize 
the ordinary surface runoff, greatly reduce the total quantity 
of water finding its way into the streams. 

SEEPAGE FLOW 

The water contributed to streams as seepage flow consists 
of ground-water supplied by percolation. Not all the percolating 
precipitation, however, appears in the streams. Some of it 
is lost through evaporation, some through transpiration, and 
on some wathersheds another, though usually small portion, 
is lost through deep seepage. When, through evaporation and 
transpiration losses, the capillary water, amounting to from 
half an inch in sand to three inches, per foot depth, in heavy 
clay, has become depleted, percolation must first replenish 
the capillary water before the soil will permit gravity to draw 
water down into the ground-water reservoir which supplies 
the seepage flow of streams. 

Effect of Watershed Characteristics. — To be possessed of 
good seepage flow, a watershed must be of such a character 
that not only will the percolation of rainfall be large, but sub- 
sequent evaporation and transpiration losses small. When 
the precipitation is ample, the soil and underlying rock strata 
are usually the most important factors influencing seepage 
flow. Even on steep slopes, deep, sandy soil and subsoil will 
permit a large amount of percolation and will quickly carry 



RUNOFF 



285 



the percolating water to depths from which it is safe against 
return by capillary action. On such watersheds, all forms 
of vegetation, by reducing the moisture content of the surface 
soil, inevitably reduce the seepage flow. 

Clay soils retard percolation, facilitate surface runoff and 
exert a large capillary lift in bringing moisture to the surface 
again for evaporation and transpiration. 



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Fig. 181. — (A) Soil Moisture in Heavy Soil at Akron, Colorado, and {B) 
Precipitation, June and July, 1909. 

The effect of even moderately heavy soil in preventing deep 
percolation is well shown in Fig. 181 from Bulletin No. 201, 
Bureau of Plant Industry and Department of Agriculture. The 
moisture indicated in the diagram is that available for plant 
growth in the given soil. It will be noted that during the 
entire period, the moisture content did not change below a 
depth of 3 feet and the heavy rain of 2.4 inches on July 7 
did not penetrate below a depth of 18 inches. The increase 
in moisture content of the upper 18 inches of soil indicates 
that nearly half of the precipitation ran off into the streams. 
Under such conditions as these, there is no ground-water supply 
and hence the small streams, at least, are necessarily intermittent. 
The season's records for this region indicate that practically 



286 ELEMENTS OF HYDROLOGY 

no surface runoff results from a rainfall of less than ^ inch. When 
from \ to 1 inch of rain falls in a short time, about a tenth of an 
inch runs off, and when over 1 inch falls in the course of a day 
from two to five tenths of an inch runs off. 

Swamps and marshes decrease both surface and seepage flow. 
Wet-weather ponds, particularly on rolling, sandy watersheds, 
increase seepage flow as they are merely depressions that be- 
come filled during rains and soon disappear, largely through 
percolation. On clayey watersheds wet- weather ponds may 
disappear mainly through evaporation. Swamps and marshes 
on very flat, clayey watersheds usually yield little runoff when 
the annual rainfall does not considerably exceed 20 inches. 

By intercepting percolating water that has already reached 
a point several feet below the surface of the ground in«its path 
toward the ground-water reservoir, tile drainage reduces seepage 
flow. 

Where impervious rock strata, sloping with the valley, under- 
lie glacial drift, and where such rock strata outcrop in the river 
bed, there is usually a large increase in seepage flow for some 
distance upstream from the point of outcrop. 

Effect of Character of Precipitation. — When the precipitation 
is insufficient to keep the ground continually moist, which is 
usually the case, the character and rate of precipitation are 
the factors which most largely influence seepage flow. When 
there is no frost in the ground, or the ground was relatively 
dry when it froze, slowly melting snow permits of the greatest 
percolation. On the whole, a greater proportion of snowfall 
than of rainfall eventually percolates into the ground to supply 
seepage flow. 

Next to snowfall in effectiveness in replenishing the ground- 
water supply are the slow drizzling rains that occur over large 
portions of the country during spring and fall when both tran- 
spiration and evaporation demands are relatively small. It 
is not unusual for the entire summer precipitation to be held 
in the upper layers of soil as capillary water, or to run off 



RUNOFF 287 

into the streams over the surface of the ground, none of it per- 
colating to supply seepage flow. 

Changes in Seepage Flow Following Percolation. — Just 
before the spring break-up in the Northwest, the seepage flow 
which, together with the outflow from lakes, constitutes the 
entire flow of streams during the winter months when the pre- 
cipitation is all stored on the surface of the ground as snow, 
has reached its minimum and has also become quite uniform. 
The increase in seepage flow which will result from a given 
increase in ground-water supply, through percolation, will de- 
pend upon the slope of the ground-water surface and the resist- 
ance of the subsoil to the flow of water. As previously stated, 
the flow of ground-water is directly proportional to the head 
and to the square of the effective size of the grains of the 
conducting material. Fine-grained subsoil,* by offering great 
resistance to flow, will maintain the ground-water table at a 
very much steeper slope than coarse-grained material. Character 
of subsoil, then, is a far more important factor in determining 
the shape of the water-table than ground surface topography. 

As the ground-water rises, by capillarity, several feet above 
the level of saturation as is well shown in Fig. 182, and as the 
plane of saturation is usually so far below the ground surface 
as to protect the ground-water from evaporation, and from 
transpiration of all plants except possibly forest trees, equal 
amounts of percolation must raise the level of saturation by 
uniform amounts in any given soil. Fig. 182 shows that a given 
amount of percolation will raise the plane of saturation 80 per 
cent more in clayey soil than in fine sand and 10 to 15 per cent 
more in fine sand than in coarse. As the head causing flow 
in the fine sand is about ten times as great as that causing 
flow in the coarse sand, the increased head due to a given 

* For the purposes of hydrology, the author uses the term "soil" to mean 
the upper layers of earth from which most plants primarily derive their suste- 
nance, i.e., the upper three or four feet. The term "subsoil" is applied to all 
the intermediate layers of earth between the soil and the underlying rock 
strata. 



288 



ELEMENTS OF HYDROLOGY 



amount of percolation has proportionately much less effect 
in increasing seepage flow in the case of the fine sand or clay. 
A given amount of percolation, then, will result in a much greater 
increase in seepage flow in the case of the watershed underlain 

PERCOLATION REQUIRED TO RAISE WATER-TABLE ONE FOOT 

Coarso Sand 



Pine Sand 



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Fig. 182. — Rise of Ground-water by Capillarity, and Percolation required 
to raise Water-table One Foot in Different Soils. 



with coarse material. It follows from this, that a watershed 
in which the plane of saturation usually lies in coarse, porous 
material will experience the greater variation in seepage flow. 



RUNOFF 



289 



Depth of Water-table. — On some watersheds the water- 
table lies so close to the surface of the ground that some of the 
ground-water is held back during the frozen season, resulting 
in minimum stream flow during the sub-zero weather of mid- 
winter. On other watersheds, there is no well-defined water- 
table except at elevations below the water courses. Streams 
draining such watersheds, particularly if lying in regions where 
the ground remains frozen during several months, often reach 
a stage of zero flow. 




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Fig. 183. — Effect of Barometric Pressure on Flow of Spring (after King). 



Effect of Barometric Pressure. — King * found that the flow 
of water from springs, , tile drains and artesian wells reflected 
changes in barometric pressure. This fact is well shown in 
Fig. 183. Although the diagram is not fully dimensioned, 
yet the synchronism of the phenomena is clearly shown. Re- 
duced pressure results in increased flow from springs and wells. 

A phenomenon intimately related to the flow of water from 
springs is the " breathing " of wells. One of the best of the 
available records of this kind is that published in the Monthly 
Weather Review of February, 1916. The essential data are 

* King, F. H., 19th Annual Report, TJ. S. G. S., p. 73. 



290 



ELEMENTS OF HYDROLOGY 



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RUNOFF 



291 



presented graphically in Fig. 184. With very few exceptions 
the air moved into the well when the barometric pressure was 
rising and out when it was falling. 

RUNOFF FROM TYPICAL WATERSHEDS 

Climatological, topographical and, to some extent, also, 
cultural conditions on a watershed, are reflected in the flow of 
its' streams. Figs. 185 to 194 show the monthly mean tempera- 




Jan. Feb. Mar. Apr; May June July Aug. Sept. Oct. Nov. Dec. 

Fig. 185. — Temperature, Precipitation and Runoff, Mississippi River 
Watershed, Minneapolis, Minn., 1897-1913. Area, 19,500 sq. mi. 



ture, precipitation and runoff for typical watersheds in widely 
different sections of the United States, for the purpose of illus- 
trating the effect of temperature and precipitation on the total 
amount of runoff. 



292 



ELEMENTS OF HYDROLOGY 




Jan. Feb. Mar. Apr. May June July Aug. Sept. Oct. Nov. Dec. 

Fig. 186. — Temperature, Precipitation and Runoff, St. Croix River Water- 
shed, St. Croix Falls, Wis., 1901-1912. Area, 5930 sq. mi. 



100 10 
90 9 




Fig. 187. 



Jan. Feb. Mar. Apr. May June July Aug. Sept. Oct. Nov. Dec. 

— Temperature, Precipitation and Runoff, Ohio River Watershed, 
Wheeling, W. Va., 1891-1905. Area, 23,820 sq. mi. 



RUNOFF 



293 




Jan. Feb. Mar. Apr. May June July Aug. Sept. Oct. Nov. Dec. 

Fig. 18S. — Temperature, Precipitation and Runoff, Tohickon Creek Water- 
shed, Point Pleasant, Pa., 1887-1911. Area, 102 sq. mi. 




Sept. Oct. Nov. Dec. 

— Temperature, Prescription and Runoff, James River Watershed, 
Cartersville, Va., 1898-1905. Area, 6230 sq. mi. 



294 



ELEMENTS OF HYDROLOGY 




Jan. 



Feb. Mar. April May June July Aug. Sept. Oct. Nov. Dec. 

Fig. 190. — ■ Temperature, Precipitation and Runoff, Tombigbee River 
Watershed, Columbus, Miss., 1900-1909. Area, 4440 sq. mi. 




Jan. Feb. Mar. April May June July Aug. Sept. Oct. .Nov. Dec. 



Fig. 191. — Temperature, Precipitation and Runoff, Colorado River Water- 
shed, Austin, Texas, 1901-1910. Area, 37,000 sq. mi. 



RUNOFF 



295 




Jan. Feb. Mar. April May June July Aug. Sept,- Oct. Nov. Dec. 

Fig. 192. — Temperature, Precipitation and Runoff, Sacramento River 
Watershed, Red Bluff, Cal., 1902-1911. Area, 10,400 sq. mi. 




Jan. Feb. Mar. Apr. May June July Aug. Sept. Oct. Nov. Dec. 

Fig. 193. — Temperature, Precipitation and Runoff, Pit River Watershed, 
Bieber, Cal., 1903-1908. Area, 2950 sq. mi. 



296 



ELEMENTS OF HYDROLOGt 




Jan. Feb. Mar. Apr. May June July Aug. Sept. Oct. Nov. Dec. 
Fig. 194. — Temperature, Precipitation and Runoff, McCloud River Water- 
shed, Gregory, Cal., 1902-1908. Area, 608 sq. mi. 



RUNOFF 297 

Watersheds in the Northwest. — The Mississippi River, 
Minnesota, and the St. Croix River, Wisconsin, watersheds are 
typical of those in the Northwest. They are characterized 
by great fluctuations in temperature and precipitation. A 
variation of nearly 60 degrees in monthly mean temperature 
is shown, with five months of the year averaging below freezing 
and midsummer temperatures reaching about 70 degrees. The 
precipitation during the five, winter months amounts to only 
about 6 inches, most of which, however, accumulates as snow 
and ice. The precipitation during the seven summer months 
aggregates about 24 inches, most of which evaporates or is 
used by plants in transpiration. Winter stream flow is main- 
tained almost entirely by ground-water. 

Watersheds in the East. — The Ohio River, Tohickon Creek, 
Pennsylvania, and James River, Virginia, watersheds are charac- 
terized by relatively small variations in precipitation and with 
winter temperatures near or above the freezing point. Little 
of the winter precipitation accumulates and as the evaporation 
loss is small and the transpiration loss is zero, the winter runoff 
is high. During the summer months the relation between 
rainfall and runoff is not widely different from that shown by 
the watersheds of the Northwest. Lower precipitation on the 
Ohio River watershed during the fall results in less runoff than 
from the James and the Tohickon. 

Southern Watersheds. — The Tombigbee, Mississippi, and 
Colorado River, Texas, watersheds are typical of a variety of 
southern watersheds. The Tombigbee River watershed shows 
relatively uniform distribution of precipitation. The Colorado 
River watershed shows a distribution somewhat similar to that 
in the Northwest. The effect of high temperatures, however, 
is clearly evident. 

If the Minnesota precipitation occurred at Texas temperatures, 
the runoff from the upper Mississippi River watershed would be 
about the same as that shown for the Colorado; and if the 
Colorado precipitation occurred at Minnesota temperatures, 



298 ELEMENTS OF HYDROLOGY 

the runoff from the Colorado River watershed would be quite 
comparable to that now observed on the upper Mississippi. 

The precipitation over the Colorado River watershed is rela- 
tively small and occurs during the warmer portion of the year. 
The temperature is so high the year around that most of the 
precipitation evaporates or is used by vegetation. Practically 
the entire runoff results from excessive rains over restricted 
areas. The water-table is far below the bed of the streams, so 
that seepage flow is substantially nil. 

High summer and fall temperatures on the Tombigbee River 
watershed together with high transpiration loss from the 
heavily forested area, result in very low summer and fall runoff. 
Soil storage having been depleted, the fall rains are mainly 
absorbed, resulting in low stream flow until well into the 
winter. 

Western Watersheds. — The Sacramento River and its trib- 
utaries, the Pit and the McCloud, are typical western streams. 
The precipitation on these watersheds is very unequally dis- 
tributed. By far the greater portion occurs during the cooler 
months. Other conditions being equal, watersheds on which 
the precipitation is distributed as shown for the Sacramento 
River suffer the least possible evaporation and transpiration 
losses. Those on which the precipitation is distributed as on 
the Tohickon Creek watershed suffer a greater loss, and those 
on which the precipitation is distributed as on the upper Missis- 
sippi watershed show by far the greatest loss of water through 
evaporation and transpiration. 

The Sacramento River also shows the effects of melting snows 
in the mountains, in maintaining stream flow during the dry 
season. The high summer flow of its snow and spring-fed 
mountain tributary, the McCloud, is particularly prominent. 

The temperatures shown for the McCloud River watershed 
are undoubtedly higher, and the precipitation somewhat lower, 
than the true average for the watershed on account of the 
fact that a considerable portion of the drainage basin consists of 



RUNOFF 299 

mountain peaks higher in elevation than the highest meteoro- 
logical observation stations for which records were available. 

The Pit River watershed has very low precipitation but a 
reasonably good runoff on account of the greater portion of the 
precipitation occurring during the winter when the temperature 
ranges around the freezing point. The physical characteristics 
of the above-mentioned watersheds are given on pp. 1103 to 1109, 
Trans. Am. Soc. C. E., Vol. LXXIX (1915). 

Hydrographs of Daily Discharge. — While monthly mean 
values of runoff, such as those given in Figs. 185 to 194, convey 
considerable information relative to the interdependence of 
the two principal factors modifying the amount of water which 
different watersheds yield as runoff, namely precipitation 
and temperature, hydrographs showing the daily discharge 
of streams, alone, can demonstrate the effect of watershed 
characteristics. Such hydrographs of typical streams are 
shown in Figs. 195 to 203. The location of the watersheds of 
these streams is shown in Fig. 204. So far as possible, streams 
draining watersheds having about the same mean annual pre- 
cipitation and temperature have been selected, so that differences 
in precipitation and temperature might not veil the effects of the 
physical characteristics of the different watersheds. Figs. 195 
to 203 bring prominently to one's attention the tremendous 
diversity of stream flow represented by this group of water- 
sheds chosen from such a restricted area as Minnesota and 
western Wisconsin. By selecting streams from different parts 
of the United States a still greater diversity of flow could, of 
course, be shown. None of the streams for which hydrographs 
are presented in Figs. 195 to 203 are located in a region of high 
precipitation. None of them drain rugged, mountainous ter- 
ritory; neither are any of them snow or glacier fed. 



300 



ELEMENTS OF HYDROLOGY 



January February March April May June July August Sept. October Nov. December 
.. 1 10 20 31 10 20 29 10 20 31 10 20 30 10 20 31 10 20 30 10 20 31 10 20 31 10 20 30 10 20 31 10 20 30 10 20 31 







































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Fig. 195. — Hydrographs of Daily Discharge. 

Red Lake River at Thief River Falls, Minn. (Below mouth of 

Thief River.) 

Watershed area, 3430 square miles. Topography flat; 15% to 20% of it lake area. Largest 
lake in upper portion of watershed. Clay loam soil with clay subsoil. Dense timber, mostly 
coniferous, over eastern three quarters of watershed and prairie, much of it open marsh over 
remainder. Little land under cultivation. About three fourths of the watershed is swamp or 
lake area. Annual rainfall: mean, 24 in.; 1911, 20 in.; 1912, 19 in. 



January February March April May June July August Sept. October Nov; December 
_1 10 20 31 10 202910 20 31 .10 20 3010 20 31 10 20 30 10 20 31 10 20 31 10 20 30 10 20 31 10 20 30 10 20 31 



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L^l 



Fig. 196. — Hydrographs of Daily Discharge. 
Crow Wing River at Pillager, Minn, (including Long Prairie). 

Watershed area, 3230 square miles. Topography gently undulating; about 2% lake area 
and practically no swamp. Sand, gravel and clay soil. Dense, coniferous forests over upper 
portion and less dense over most of the remainder, with some land under cultivation in southern 
portion of basin. Most of watershed logged over, but second growth dense. Annual rainfall: 
mean, 26 in.; 1911, 25 in.; 1912,22 m. 



RUNOFF 



301 



January "February March April May June July August Sept. October Nov. December 
.1 10 20 31 10 20 2910 20 31 10 20 30 10 20 31 10 20 30 10 20 31 10 20 31 10 20 30 10 20 31 10 20 30 10 20 31 



§ 1- 

K 1. 

c 0. 
"S 0. 

«a 

•a 0. 
§1. 
8 l. 
?l. 

§0. 

■s 0. 

s°- 

Fig. 197. — Hydrographs of Daily Discharge. 
Clearwater River at Red Lake Falls, Minn. 

Watershed area, 1310 square miles. Topography flat; less than 1% lake area. Soil clay loam 
with clay subsoil. Little cultivated land. Dense timber, mostly coniferous, over eastern 
two thirds of watershed and prairie with much marsh land over western one third. Estimated 
general slope about 3 ft. per mile. Annual rainfall: mean, 24 in.; 1910, 13 in.; 1911, 20 in. 




C January 'FebrTiafy' March April May June July August Sept. October Nov. December 
*2 , ,- 1 10 20 31 10 20 29 10 20 31 10 20 30 10 20 31 10 20 30 10 20 31 10 20 31 10 20 30 10 20 31 10 20 30 10 20 31 
u }. 
g . 
°"1 
t. 1. 

So. 

o 0, 
"So. 

73 0, 

B 1 
gl. 

&> 

Car 
«2 

■so. 
»o. 

a 

Fig. 198. — Hydrographs of Daily Discharge. 
Ottertail River at Fergus Falls, Minn. 

Watershed area, 1310 square miles. Topography prominently rolling, morainic, and knolly. 
About 15% lake area. Largest lake in lower portion of watershed. Soil varying from clay 
to sand and gravel. Upper portion of watershed lightly timbered. Southern portion largely 
under cultivation. Annual rainfall: mean, 25 in.; 1910, 14 in.; 1911, 24 in. 



50 
.25 

no 


















































































































































































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00 
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302 



ELEMENTS OF HYDROLOGY 



January February March April May June July August Sept. October Nov. December 
1 10 20 31 10 20 29 10 20 31 10 20 30 10 20 31 10 20 30 10 20 31 10 20 3110 20 30 10 20 31 10 20 30 10 20 31 
. 2.00- 



SS 



,,71.00 



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91 


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-\- 
















A 


























M 









January February March April May June July August Sept. October Nov. Decemi] 
10 20 31 10 20 20 10 20 31 10 20 30 10 20 31 10 20 30 10 20 31 10 20 31 10 20 30 10 20 31 10 20 30 10 20 3 


er 
1 
























































































































































































































8.00 




































































- 




























































































































































































































7.00 
















































































































































§ 
















































































































































s 

§ 6.00 

OS 


























































































































































































































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60 

U 3.00 


















































































































































o 

CO 










































































p 




































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0.00 


b 


^ 


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- 


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r 4 






I 


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Fig. 199. — Hydrographs of Daily Discharge. 
Elk River near Big Lake, Minn. 

Watershed area, 615 square miles. Topography flat to gently rolling with occasional sand and 
gravel hills and less than 1% lake area. Soil black loam often quite sandy, with clay, sand, 
and gravel subsoil. Nearly all land under cultivation. Annual rainfall: mean, 28 in.; 1911, 
32 in.; 1912, 29 in. 



RUNOFF 



303 



January February March April Slay June July August Sept. October Nov. December 
1 10 20 31 10 20 29 10 20 31 10 20 30 10 20 31 10 20 30 10 20 31 10 20 31 10 20 30 10 20 31 10 20 30 10 20 31 















































































































































































































14.00 














































































































































































































































































16.00 














































































































































































































































































12.00 














































































































































































































































































1.00 














































































































































































































































































0.00 




































































































































- 






































































































































9.00 














































































































































































































































































8.00 














































































































































































































































































7.00 














































































































































































































































































G.00 


























































































































































































































































































































































































































































































































































4.00 














































































































































































































































































3.00 






































































































































































































































19 


11 






































3.00 








































































































































































































































































1*00 
























































































































































































1 


























M 
































n.no 































































Fig. 200. — Hydrographs of Daily Discharge. 
Root River at Lanesboro, Minn. 



304 



ELEMENTS OF HYDROLOGY 



January February March April. May June July August Sept. October Kov. December 
,1 10 20 31 10 20 29 10 20 31 10 20 30 10 30 31 10 20 30 10 20 31 10 20 31 10 20 30 10 20 31 10 20 30 10 20 31 



.12.00 



11.00 



10.00 



9.00 



§8.00 



M7.00 



^0.00 



«>5.00 



14.00 



3.00 



2.00 



1.00 



0.00 

Fig. 201. — Hydrographs of Daily Discharge. 
Root River at Lanesboro, Minn. 

Watershed area 647 square miles. Topography relatively flat to gently undulating but 
streams flow through wide, deep, V-shaped valleys; that of main stream being several miles 
in width and several hundred feet below general level of surrounding country. No lakes. 
Soil clayey loam with clay subsoil and water-table far below surface of ground. Underlying 
sandstone rocks outcrop in river bed. Average slope of stream about 8 ft. per mile. Annual 
rainfall: mean, 30 in.; 1911, 45 in.; 1912, 30 in. 





































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































191: 




















































































































































































































































































































_ 




- 


- 




















































" 


- 


1 









































RUNOFF 



305 



6.00 



January February March April May June July" August Sept. October "Nov. December 
1 10 20 31 10 20 29 10 20 31 10 20 30 10 20 31 10 20 30 10 20 31 10 20 31 10 20 30 10 20 31 10 20 30 10 20 31 



= 5 
3 



00 























































































































































































































































































































































































































































































































































































































































































































































































































































: 


914 








































































































































































































































































i 




























- 










































































iii i 


















.- 


-. 




9 


- 






// 
















. 




: - 










--ft 













































93 4.00 



3.00 



2.00 



pl.00 



0.00k 

Fig. 202. — Hydrographs of Daily Discharge. 
Wisconsin River between Rhinelander and Merrill. 

Watershed area, 1520 square miles. Topography rolling with considerable number of lakes; 
about 5% of watershed under reservoir control. Soil quite sandy. Considerable land under 
cultivation; remainder covered with second growth. About half of land was burned over in 
1909 to 1913. Most of lakes at upper end of streams. Annual rainfall: mean, 32 in.; 1914, 
34 in. 



306 



ELEMENTS OF HYDROLOGY 



Jan. Feb. Mar. Apr. May June July Aug. Sept. Oct. Nov. Dec. 
1 10 20 31 10 20 29 10 20 31 10 20 30 10 20 31 10 20 30 10 20 31 10 20 31 10 20 30 10 20,31 10 20 30 10 20 31 



15.00 



14.00 



13.00 



12.00 



11.00 



10.00 



2 9.00 



8.00 



7.00 



6.00 



5.00 



4.00 



3.00 



2.00 



1.00 



0.00 



Fig. 203. — Hydrographs of Daily Discharge. 
Black River at NeillsviUe, Wis. (1914). 

Watershed area, 772 square miles. Topography distinctly rolling with no lake area. Soil 
rather clayey. Considerable land under cultivation. Timber mostly second growth. Streams 
in narrow V-shapcd valleys. Average slope along stream about ft. per mile. Annual rainfall: 
mean, 33 in.; 1911, 3S in. 




RUNOFF 307 

The watershed characteristics essential to an interpretation 
of these hydrographs are briefly summarized under each figure. 
Both the Red Lake and the Clearwater Rivers drain large 
swamp areas. While these swamps have a tendency to equalize 
the stream flow, to some extent, their principal effect is to so 
increase evaporation and transpiration losses as to greatly 
reduce the total amount of runoff. Heavy precipitation on 
the Clearwater River watershed during 1909 and in the spring 
of 1910 resulted in heavy runoff during the 1910 break-up. 
Light precipitation during the remainder of 1910 and during 
1911 resulted in very low runoff during that period. 

The fact that sandy soils and lakes, in more rolling country, 
not only equalize stream flow, but conserve the rainfall far better 
than timbered swamps and marshes is clearly shown by compar- 
ing the discharge of the Red Lake and the Clearwater Rivers 
with that of the Crow Wing and the Ottertail, respectively. 
The watersheds of these streams are almost exactly equal in 
size, yet show a most striking diversity of flow. After the freeze- 
up in November, 1911, the discharge from the Red Lake water- 
shed dropped to between five and ten cubic feet per second and 
remained so throughout the entire winter. For two entire 
years, from September, 1910, to August, 1912, the principal 
tributary of the Red Lake, i.e., the Thief River, with a tribu- 
tary watershed of over 1000 square miles, most of which is 
swamp and much densely timbered, yielded a total runoff of 
only .11 inch in depth over the watershed. 

The June, 1911, freshet on the Red Lake River resulted from 
about 4 inches of precipitation during the month. The May, 
1912, freshet on the Crow Wing River resulted from about 
6.5 inches of precipitation during that month. 

The Elk and the Root River watersheds are quite similar 
in surface topography. The differences shown by the hydro- 
graphs result mainly from the more sandy character of the soil 
on the Elk River watershed. 

The rainfall on the Root River watershed in 1911 was very 



308 ELEMENTS OF HYDROLOGY 

much heavier than on the Elk. The 1912 precipitation was 
very nearly the same on both watersheds. The precipitation 
which caused the freshet of May, 1912, on the Elk River, shown 
in Fig. 214, was almost as large as that which caused the August, 
1911, flood on the Root River, shown in Fig. 215. The March- 
April, 1912, break-up was not accompanied by heavy rains on 
either watershed. The small rise on the Elk River is, to a large 
extent, due to lesser soil and subsoil storage as indicated by the 
lower winter flow. Both streams show an exceptionally well 
sustained low-water flow. 

While the Wisconsin River watershed between Merrill and 
Rhinelander is about twice as large as the Black River water- 
shed at Neillsville, and would, therefore, be expected to show 
slightly less sudden fluctuations in stream flow, nevertheless, 
the differences shown result, primarily, from the more sandy 
character of the soil on the Wisconsin River watershed and the 
steeper slopes on the Black River. The regimen of these streams 
is somewhat similar to that of the Elk River and the Root River, 
respectively, although the Root River has a better low-water flow 
on account of the underlying sandstone rock that outcrops in 
the river bed. 

The extraordinary flood on the Black River, in June, 1914, 
resulted from very exceptional precipitation (see Fig. 212) 
averaging 3.92 inches in 24 hours. In July, 1912, a precipitation 
of 5.15 inches in 24 hours produced a flood flow of 27.5 c.f.s. 
per square mile from the Wisconsin River watershed between 
Rhinelander and Merrill. A map of the rainfall causing this 
flood is shown in Fig. 213. 

THE FLOOD FLOW OF STREAMS 

Most streams of the country are subject to considerable 
variation in stage. Under normal conditions the discharge is 
carried within well-defined banks but, periodically, most streams 
experience a runoff from the tributary watershed which is greater 
than can be carried at a bank-full stage. At such times the 



RUNOFF 309 

stream leaves its banks and spreads out over its valley. As 
a river usually carries considerable detritus in times of flood 
and as the shallower water outside of the banks has a slower 
velocity than that within the banks, the sediment is deposited, 
forming the well-known alluvial flood plain. The very presence 
of such a flood plain is conclusive evidence of prevalent floods. 

In the development of the country, however, many people 
have too often associated such physiographic features as this 
with ancient geologic ages and have attempted to occupy the 
river's flood plain, only to find their structures destroyed and 
their fields laid waste. The fertility of the alluvial valley 
and its accessibility through the river channel, when other 
means of communication were wanting, coupled with the 
relatively infrequent occurrence of devastating floods and the 
optimism of flood sufferers, have been irresistible inducements 
to occupation. 

Floods Due to Rainfall 

Flood Producing Rains. — As floods originate in precipitation, 
its amount and distribution are of primary importance. Floods 
may result from either rainfall, snowfall, or a combination of 
the two. 

Flood producing rains are not limited to regions of high annual 
precipitation; in fact, torrential rains, though less frequent, 
are, nevertheless, common in the arid and semi-arid West. 
The smaller the watershed tributary to a stream, the more 
intense and concentrated the precipitation required to produce 
a flood stage. Protracted general rains, that produce only 
moderate stages in the minor water courses, cause floods on 
the main stream. Torrential rains, commonly called "cloud- 
bursts," that have little effect on the main stream, cause floods 
on its tributaries. In general, the maximum flood due to rain 
will result from the greatest amount of most unfavorably dis- 
tributed precipitation which may be expected to occur over 



310 ELEMENTS OF HYDROLOGY 

the entire tributary watershed within the time required for 
water from the remotest portion of the drainage basin to reach 
the point of observation. The time of concentration, in turn, 
depends upon the topography of the watershed and the size 
and slope of the water course. 

Intense Rainstorms as Basis for Flood Estimates. — Records 
of runoff will, for a good many years, be far more incomplete, 
in most parts of the United States, than records of rainfall. 
By making a thorough analysis of all available rainfall and run- 
off data, a better judgment can be formed of the probable 
extreme flood flow of a given stream, than if observed stream- 
flow data, alone, are relied upon. A study of the most intense 
rainstorms in the part of the country under investigation should 
first be made. The measure of intensity of storms must in- 
clude both watershed area and average precipitation over that 
area, together with its distribution. The rainfall which caused 
the greatest recorded flood on the given stream should then be 
mapped and studied in connection with the resulting flood dis- 
charge. A comparison of the given rainstorm with the most 
intense storm to be expected within the locality under consid- 
eration will then afford a basis for estimating the probable 
extreme future flood. The frequency of occurrence of extreme 
floods, however, must remain a matter of uncertainty until 
very much more data are available. 

Effect of Watershed Area. — Perhaps the most important 
single factor influencing the flood flow of a stream is the size 
of its tributary watershed. The reason lies in the variation 
of precipitation with area. Torrential rains aggregating five 
to ten inches in a day, or less, occur only over relatively small 
areas, because the available moisture supply of the air on a 
summer day, if uniformly precipitated over the entire conti- 
nent, would amount to very much less than this. Excessive 
precipitation over a small drainage basin is possible only at the 
expense of precipitation on the adjoining watersheds. So pro- 
nounced is the effect of watershed area on flood flow, that widely 



Mi. 



Dit 






n 



RUNOFF 311 

scattered watersheds of equal area but of dissimilar topograph- 
ical characteristics experience quite similar flood flows. 

Differences in precipitation over a large watershed result 
in irregularities in stream flow on the tributaries that are com- 
pletely smoothed out when the main stream is reached. This 
is well shown by the hydrographs, Fig. 205, of the Mississippi 
River at Anoka, Minnesota, and of its principal tributaries. 

Reasonably heavy, but irregularly distributed rains occurred 
on the watershed between May 3 and 5 as shown in Fig. 206. 
As a result of these rains a flood of somewhat more than ordinary 
magnitude for the main stream crested at Anoka, Minnesota, 
on May 8. None of the large tributaries, except the Elk and 
the Rum rivers, experienced more than an ordinary flood. 
The time of cresting of this flood at Anoka seems to have 
been determined mainly by the discharge of the Elk and the 
Rum rivers and of the minor tributaries aggregating about 35 
per cent of the total watershed area. 

Of the larger tributaries, the Crow Wing crested before the 
main stream, and the Sauk and Crow rivers crested after it, 
and thus prolonged the flood, although they did not increase 
it. The effect of the upper Mississippi reservoirs is well shown 
by the uniform discharge of the main stream just below the four 
main reservoirs, and by a comparison of the hydrograph showing 
the runoff from the entire watershed above Anoka with that 
from the watershed below the reservoirs. 

Effect of Shape and Location of Watershed. — A fan-shaped 
drainage area that permits the water from several equal-sized 
tributaries to reach the main stream at the same time, and an 
elongated area draining in the direction the storm moves will, 
in general, experience more serious floods than more irregularly 
shaped areas. Most streams like the Ohio draining in the oppo- 
site direction from that in which the storm moves, have far less 
severe floods than if they drained in the other direction. Streams 
draining to the north have more severe spring floods than those 
draining to the south on account of the gorging of the lower, 



Discharge- Discharge- Discharge- Dto 

Sec. Ft. per Sq. Ml. Sec. Ft. per Sq. Ml Sec. Ft. per Sq. Ml. Sec. Ft. per Sq. Mi. 




Discharge — 
Diuoharge-Sec.rt.perSq.'Hi. Sec. Ft. per 8q\ ML Discharge-Sec. Ft. jwrSq. Ml. 

cBBe-BeEB-SBEBeEB 



: ,M 

s P°^B 

S2 I J 

Buz 
s ™^ 

8 H^— — 




Discharge— Disohorge- 

Seo. Ft. per Sq. HI. Sec. Ft. per E 

g g 



- 








» 






■ 






* 






a 






=■ 












» 






=1 






3 Bji 
8 |° 






|_ 




312 



ELEMENTS OF HYDROLOGY 




St.Paul 



WATERSHED OF MISSISSIPPI RIVER 

AND ITS PRINCIPAL TRIBUTARIES 

ABOVE ANOKA, MINNESOTA 

WITH ISOHYETALS FOR MAY 3-5, 1912 

Fig. 206. 



RUNOFF 313 

frozen-up reaches of the stream, with water running off from 
the warmer, more southerly portion of the drainage basin. 
This is well illustrated by the Red River of the North. 

Effect of Soil. — Clay soil or rock outcrops and steep slopes 
result in the rapid concentration of flood waters. Pervious 
soil and flat slopes give the floods of a stream draining a small 
watershed many of the characteristics of one draining a much 
larger area. This is illustrated by the Crow Wing River 
watershed. 

Effect of Cultural Conditions. — When flood producing rains 
fall on a watershed, cultural conditions, such as forest cover, 
have little effect in retarding the flow. At best, they are of 
secondary importance. Forests may contribute to floods by 
retarding the melting of snow as illustrated by the Little Fork 
River watershed. 

Watershed Characteristics Reflected in Floods. — Differences 
in watershed characteristics are prominently reflected in the 
flood hydrographs of the Root, Elk, Black, Wisconsin and 
Wild Rice rivers, Figs. 207 to 211. Of these five streams the 
Black River discharged the most water, although the rainfall 
on the watershed was least. The physical characteristics of the 
Black River watershed are given on page 306. The absorptive 
character of the Wisconsin River watershed, notwithstanding 
moderately steep slopes, is well shown by the hydrograph of 
that stream. Maps of the rainfall which caused the floods 
on the Black and the Wisconsin rivers are given in Figs. 212 
and 213. 



314 



ELEMENTS OF HYDROLOGY 



"May 

10 11 12 13 14 15 16 17 









































MAY; 1912, FLOOD, 

ELK RIVER 

AT BIG LAKE, MINN. 

Watershed - 615 sq.mi. 





































































































7* i 

v ■ 

?-5i Wi- 
rt a H ■ 

5 3 I 

" aoML 



Fig. 207. 







12 


IS 


14 


15 


Augus 
16 17 


18 


19 


30 


2! 


4.64 
























•d 


- |a» 

CO 

c. 

- §15 

CO 
A 

- Sio 
fa 

3 
o 

- i 5 

is 
a 

J3 






















S« 1 

an ■ 

?j 1 








AUGUST, 1911, FLOOD, 

ROOT RIVER 

AT LANESBORO, MINN. 

Watershed - fit" sq.mi. 


O m 1 

s = 1 






















^ u 1 
Sim 1 
* ' 1 


















< 




















S 




















I 


"iQ 


2 


18. 











T a 1j37 

n I 



RUNOFF 



315 



June, 19H 
C 7 8 91011 12 13 




Fig. 209. 



U 3 

5 — 



1=1-1 

gM.11 

O 



30 



225 



•a 20 



•sio 



July 1912 Augr. 

23 24 25 26 27 28 29 30 31 1 2 































JULY, 191 2, FLOOD, 

WISCONSIN RIVER 

BETWEEN 

RHINELANDER AND MERRILL 

Watershed - 1520 eq. mi. 


















































-3 

eija 




















" a 

CO O 






















SI 



^l2l.82 
- ; ■ 

a§ I 

- ?, i 



Fig. 210. 



316 



ELEMENTS OF HYDROLOGY 



July 
19 20 21 22 23 24 25 26 27 



II 6 " 1 

** 3 
w m 

<u a 
o — 

Pi £ 



Aug. 
29 30 31 1 



JULY, 1909, FLOOD, 

WILD RICE RIVER 

AT 

TWIN VALLEY, MINN. 

Watershed - 805 sq. mi. 




Fig. 211. 



RUNOFF 



317 



• Weyerhaueer 



Stanley 



Merrill 
#2.8 



\iv$ ( 




\ \ 

V \ 




» \/ 

\ ( 

Neillsville «^ 
1.5 




s 

f / 

/ 

/ / 
/ / 




- 




Hatfield • 
1.9 








SCALE OF MILES 






Meadow Valley 

• 2.4 


10 20 30 




40 



Grand Rapida 



Fig. 212. — Medford, Wisconsin, Storm, Black River above Neillsville, 
June 3-4, 1914. One-day Storm. 

Average precipitation over Black River Watershed above Neillsville, 3.92 in. 



318 



ELEMENTS OF HYDROLOGY 



• Park Falls 
1.01 




Fig. 213. — Merrill, Wisconsin, Storm, July 23-24, 1912. Less-than-one- 

day Storm. 

Elk River Flood. — The May, 1912, Elk River flood shown 
in Fig. 207 resulted from 4.95 inches of rain over the watershed 
in three days. The physical characteristics of this watershed 
are given on page 302. The river had been moderately high 
throughout April and the ground was very moist; consequently 
there was heavy runoff, notwithstanding the normally large 
absorptive capacity of the soil of this watershed. 



RUNOFF 



319 



Root River Flood. —The Root River flood of August, 1911, 
Fig. 208, resulted from 4.64 inches of rain in 24 hours. The 
physical characteristics of this watershed are given on page 304. 
The river had been extremely low during July, but moderate 



FORT RIPLEY 
• 2.45 



COLLEGfVIL 
3.76 • 




SCALE OF MILES 



GLENCOE 

• 0.75 



ST.PAUL. 
2.37 • 



Fig. 214. — St. Cloud, Minnesota, Storm. May 3-5, 1912. 



rains had fallen early in August so that the soil was in good 
condition to absorb the heavy rainfall of August 13. While 
the total runoff was relatively less than that from the Elk River 
watershed, the steeper slopes on the Root and the concentration 



320 



ELEMENTS OF HYDROLOGY 



of the rainfall within 24 hours caused a much higher and sharper 
flood peak. 

Maps of the rainfall causing these floods are given in Figs. 
214 and 215. 



WINONA 
» 0.71 



LA CROSSE 
1.14 • 




NORTHWOOD 
0.43 • 



CLEAR LAKE MASON CITY 
0,45 • f> 1.25 



CHARLES CITY NEW HAMPTON 
» 2.20 • 2.62 



2.20 
SCALE OF MILES 



10 20 30 40 

Fig. 215. — Grand Meadow, Minnesota, Storm, August 13, 1911. One-day 

Storm. 



Wild Rice River Flood. — The storm that caused the flood 
on the Wild Rice River was the second severest recorded in 
the Northwest, so far as small watersheds are concerned. (See 
Fig. 123.) The greatest recorded storm in this region is that 
which centered at Fort Madison, Iowa, June 9 to 10, 1905. 
These two storms furnish a good basis for estimating the probable 
maximum flood flow from watersheds of the Northwest having 
an area of less than about 5000 square miles. While it is im- 
possible to say with what frequency such intense rainstorms as 
these will probably occur on any given watershed, nevertheless, 
it is safe to say that since only two storms of the given intensity 
have occurred in the Northwest during the past twenty years, 



RUNOFF 321 

notwithstanding the large number of stations at which the rain- 
fall has been observed, such storms are not to be expected on 
any given watershed with a greater frequency than, perhaps, 
once in several hundred years. 

The outstanding feature of the Wild Rice River flood, Fig. 
211, is the small runoff which resulted from the extraordinary 
precipitation on the watershed. The explanation of this fact 
is to be found in the characteristics of the watershed. The 
slopes in the basin are very gentle. The topography varies 
from morainic to flat but there is very little swamp land. About 
5 per cent of the basin is lake area. Many of these lakes have 
no outlet, their inflow evidently being lost largely by percolation. 
About 20 per cent of the drainage area is controlled by logging 
and other dams. Only the extreme upper part of the basin 
is heavily forested. The remainder consists of brush and open 
prairie, with considerable land under cultivation. The soil has 
good absorptive capacity. In the lower half of the basin 
artesian wells are found at depths of about 200 feet, in a stratum 
of sand and gravel overlain by clay. In the lower reaches of 
the main stream, several important tributaries become lost 
in the lowlands. 

The river overflowed its banks at the gaging station during 
the flood of 1909, and the discharge record is probably consider- 
ably in error as the flow was computed by Kutter's formula.* 

Scioto River Flood. — Fig. 216 shows the 1913 flood on the 
Scioto River at Columbus, Ohio. The rainfall which caused 
this flood is mapped in Fig. 217. The precipitation shown on 
this map is that which fell before the river had crested. It 
averaged 6.1 inches on the watershed. The total rainfall 
from March 23 to 31, viz., 9.54 inches, is given on the flood 
hydrograph for the purpose of comparing it with the total run- 
off during the flood. The outstanding feature of the Scioto 
flood is the fact that about 90 per cent of the rainfall appeared 

* Report of Water Resources Investigation of Minnesota, 1909 to 1912, 
p. 402. 



322 



ELEMENTS OF HYDROLOGY 



March April 

24 25 26 27 28 29 30 31 1 2 




24 25 26 27 28 29 30 31 1 2 
.March. April 

Fig. 216. 



RUNOFF 



323 



in the stream. This is due to the steep slopes and the satu- 
rated condition of the ground when the rains began.* 



Sandusky *^ 6.01 




SCALE OF MILES 



Fig. 217. — Central Ohio Storm, March 23 to 1 p.m. March 25, 1913. 
Two-and-one-half-day Storm. 



Ohio River Flood. — Fig. 218 shows the 1913 flood on the 
Ohio River at Cincinnati. The peculiar shape of the hydrograph 
is due to the fact that the flood water of the Great Miami was 
the first to reach the Ohio, at Cincinnati. The current was 
either upstream, or imperceptible, for about 36 hours. f For 

* Re Scioto Flood, see Report on Flood Protection for the City of Columbus, 
Ohio, by John W. Alvord and Charles B. Burdick, Sept. 15, 1913. 

t See Bulletin Z of the U. S. Weather Bureau, "The Floods of 1913," pp. 
25 and 26. 



324 



ELEMENTS OF HYDROLOGY 



more than two days the gage height at Cincinnati was no indi- 
cation, whatever, of the discharge of the stream. This is 
well shown by the hydrographs and the graph of fall between 
Maysville and Cincinnati, Fig. 219. Both the values of dis- 
charge given by the U. S. Geological Survey in Water Supply 
Paper No. 334, page 65, and the estimate made by the author, 
of the probable discharge of the stream, are shown on the flood 
hydrograph of Fig. 218. 







?i 


25 


26 


March 

27 28 


29 


30 


31 


1 


2 


3 


4 


5 


April 

6 7 


8 


9 


10 


11 


12 


13 




i 

a 

J 4 


.57 

B £ 
















MARCH 1913 FLOOD 

OHIO RIVER 

AT 

CINCINNATI, OHIO 














U.S.G 

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4.2-g 

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is 

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Waterehed-75,800 sq.mi. 














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Fig. 218. 



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2490 



C480 



U70 



460 



450 





















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HYDROGRAPHS OF OHIO RIVER 

DURING 

FLOOD OF MARCH, 1913 












- 















































20 21 22 23 24 25 26 27 28 29 30 31 1 2 3 4 5 6 7 8 9 10 11 
March April 

Fig. 219. 



RUNOFF 



325 



The precipitation considered in connection with the Ohio 
River flood at Cincinnati is that of the entire storm extend- 
ing from March 23 to 27, 1913, shown in Fig. 220. 




MAP SHOWING RAINFALL IN OHIO KIVER BASIN. MARCH 23.27. 1913 



From U.S.G.S. Water Supply Paper No. 334. 

Fig. 220. 



Floods Due Primarily to Snowfall 

Accumulation of Snow. — The effect of snow in producing 
flood flows depends, primarily, upon the amount accumulated, 
and the rate of melting. The watershed area has much less 
effect on the magnitude and characteristics of floods resulting 
from snow than on those resulting from rain. A number of 



326 ELEMENTS OF HYDROLOGY 

snowstorms passing over a watershed may eventually produce 
a relatively uniform, deep cover, even though each storm in 
itself may distribute its moisture quite irregularly. 

The possible accumulation of snow on a watershed is depend- 
ent both upon the amount of winter precipitation and upon 
the temperature. In some regions the snowfall is heavy, but 
the snow melts so soon after falling that little accumulates. 
In other regions the temperature continues below freezing 
for months, and the entire winter's precipitation accumulates. 

Floods on streams draining watersheds less than 1000 square 
miles in area, almost invariably result from excessive summer 
rains. The amount of snow-water likely to be suddenly released 
through high temperatures and such precipitation as may be 
expected at the time of break-up in the spring, is usually less 
than the excessive rain which occasionally falls later in the season. 

The rate of rise in temperature, particularly after the snow 
has become compacted, is an important factor influencing 
the amount of accumulated precipitation which appears in the 
streams. A progressive warming up over, a watershed decreases 
the flood heights on streams flowing south, but increases them 
on streams flowing north. A sudden warming up has the oppo- 
site effect. Forests retard the melting of snow, and, in this way, 
bring the period of break-up later into the spring when the rain- 
fall is heavier. Through this action, particularly if the ground 
was frozen through the winter, or saturated by fall rains, forests 
often increase floods, as was illustrated by the flood of the Cedar 
River, Washington, November 19, 1911, and of the Little Fork 
River, Minn., April 18, 1916. 

Melting of Snow. — Snow melting slowly from the sun's 
heat does not usually produce serious floods, as a large amount 
of the water is evaporated. On the other hand, Warm rains 
falling on cold snow, alone, will not produce high runoff, 
either. This fact is well presented by Horton * in the following 
statement : 

* Horton, Robert E., Monthly Weather Review, December, 1905. 



RUNOFF 327 

"Thus, to melt one inch of congealed water, or 
say, five inches compact snow, or ten inches loose, 
fresh snow with rain at 42 degrees, would require 
14.4 inches of rain." 
Horton states that the sun's heat will melt snow at the rate 
of about .05 inch depth of water per 24 hours for each degree 
the air temperature is above 32° F. 

Snow has great capacity for holding water by capillarity 
against gravity. If the ground under the snow is not frozen, 
or, if frozen, is not saturated, a surprisingly large amount of per- 
colation will occur when the melting process is gradual. When 
day and night temperatures both remain above freezing, however, 
for a few days, so as to reduce the snow to slush and warm rains 
then set in, the accumulated precipitation quickly finds its way 
into the streams and produces floods. 

Crow Wing River Flood. — Fig. 221, for the Crow Wing 
River, is a typical hydrograph of a flood due exclusively to melt- 
ing snow. The physical characteristics of the Crow Wing 
watershed are given on page 300. While the flood of April, 
1916, on this stream is the highest on record, nevertheless, it 
represents a comparatively small amount of runoff. Most of 
the melting snow found its way into the ground, or into lakes 
and ponds. 

Little Fork River Flood. — The flood on the Little Fork 
River, shown in Fig. 222, was due, primarily, to the heavy winter 
snowfall. It was aggravated, however, by three conditions: 

1. The heavy forests retarded the melting of the snow 

until the heavy April rains set in. 

2. The clayey soil was unable to absorb much water, 

notwithstanding the flat topography, because about 
4| inches of rain had fallen during the previous 
October and November. 

3. The stream flows northward so that the break-up 

was progressive down stream. 



328 



ELEMENTS OF HYDROLOGY 






5 1- 





11 a 

20 


rch 

:>,0 


31 


1 


2 


3 


4 


April 
5 6 


r 


8 


9 


10 


11 


12 














APRIL, 


1916, FLOOD 




















CROW WING RIVER 


















INCLUDING THE 
LONG PRAIRIE RIVER 


































AT' MOTLEY, MINN. 


















Watershed 3113 Sq.Mi. 








rt 
































c" 
02 
































P" 






























a 
































sj 
































































































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IH 



> 1.52 

i| 



Fig. 221. 



a a ' 



April May 

12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 1 _2 3 4__5_ 



APRIL 1916 FLOOD 
LITTLE FORK RIVER 

AT 
LITTLE FORK, MINN. 

Watershed-1720 sq.mi. 




0™- 



Fig. 222. 



RUNOFF 329 

After May 5, the Little Fork River fell slowly for about two 
weeks and then rose again, due to May rainfall, remaining 
practically at flood stage for about two months. 

The inability of heavy forests, when occurring on flat, clayey 
watersheds, to prevent flood runoff, is clearly shown by the 
1916 flood on the Little Fork River. On the other hand, the 
inability of these same heavy forests to produce a good low- 
water flow in dry seasons is shown by the fact that the discharge 
in September, 1910, and during the winter of 1911 to 1912, 
fell to .05 cubic foot per second per square mile. 

Effect of Temperature and Precipitation on Winter and 
Spring Floods 

Figs. 222 to 229 have been prepared to show the combined 
effect of temperature and precipitation on the flood flow of 
typical streams. 

The Ohio River at Pittsburgh. — The Ohio River watershed 
above Pittsburgh, Penn., with an area of 19,000 square miles, 
ranges from rolling to mountainous. The soil cover, on the 
whole, is thin, and the slopes are steep. Most of the watershed 
consists of brush-covered, cut-over land. Floods occur mainly 
in winter because the precipitation is quite uniformly distrib- 
uted through the year and heavy thaws may be expected at 
any time. This is clearly shown by the graphs. 

Severe floods on this stream are usually the combined result 
of warm weather and rain. High minimum temperatures 
appear to be especially effective in bringing the precipitation 
into the streams. Freezing night temperatures, notwithstanding 
high day temperatures, have a great retarding influence. This 
is evident from a study of the peaks on the hydrograph. Com- 
binations of temperature and precipitation that would result 
in still greater floods very evidently are possible. 

The maximum stage on the Ohio River at Pittsburgh was 
reached on March 15, 1907. As will be noted from Fig. 224, 
this flood resulted from a light snowfall on March 10, combined 



330 



ELEMENTS OF HYDROLOGY 



with about If inches of rain and very warm weather a few days 
later. A more serious flood, however, might easily have occurred. 
Either the snowfall of February, 1910, or the rainfall of Decem- 
ber, 1901, would have greatly increased the flood crest. 



■December 
10 20 31 



January 
10 20 



February 

10 20 29 




Fig. 223. — Ohio River Watershed, Effect of Temperature and Precipitation 
on Stage at Pittsburgh, December, 190HVlarch, 1902. 



While the 1907 flood reached the highest recorded stage at 
Pittsburgh, it was of such short duration and the lower trib- 
utaries of the Ohio, except the Green River, Kentucky, delivered 
so little water, as to result in very ordinary stages in the lower 
reaches of the stream. 



RUNOFF 



331 



The flood of March 1, 1902, was the second greatest on record, 
and conditions were favorable for a still greater flood. The win- 
ter had been cold and considerable snow had accumulated. 
The rise in temperature during the last week of February was 

December January February March 

10 20 31 10 20 31 10 20 29 10 20 31 




Fig. 224. — Ohio River Watershed, Effect of Temperature and Precipitation 
on Stage at Pittsburgh, December, 1906-March, 1907. 

rapid, the minimum reaching 44 degrees, "but very little rain fell. 
Fig. 223 clearly shows temperature conditions most favorable 
to a serious flood, and the absence of rain at the critical time. 
A situation almost equally favorable to a record-breaking 
flood existed in the spring of 1910. If the minimum temperature 



332 



ELEMENTS OF HYDROLOGY 



of 45 degrees on February 27 had been accompanied by even 
an inch and a half of rain, a great flood would have followed. 
The large amount of water that ran off, notwithstanding the 
small March precipitation, is well shown in Fig. 225. 



December January February 

10 20 31 10 20 3f 10 20 29 



March 



20 31 




Fig. 225. — Ohio River Watershed, Effect of Temperature and Precipitation 
on Stage at Pittsburgh, December, 1909-March, 1910. 

The Upper Mississippi River at St. Paul, Minn. — The 

Mississippi River at St. Paul, Minn., drains an area of 35,700 
square miles, consisting of the watershed of the Mississippi 
proper and that of the Minnesota River. The watershed con- 
sists of relatively flat and gently rolling land, considerable 



RUNOFF 333 

portions of which are distinctly sandy. At least half of the 
land is under cultivation. Only a small portion of the water- 
shed is heavily forested. Portions of the watershed drained by 
the Minnesota River are relatively flat, have a heavy clay soil 
and yield little runoff under ordinary conditions. 

The greatest flood on record is that of 1881, when a stage 
of 19.1 feet on the gage was reached, corresponding to a dis- 
charge variously estimated at from 95,000 to 120,000 second- 
feet. While the meteorological data for 1880 to 1881 are very 
meager, the flood appears to have been the result of rather 
general heavy winter and early spring precipitation. 

The second greatest flood occurred in March and April, 
1897. A stage of 18.0 feet, corresponding to a discharge of 
85,500 c.f.s., was reached on April 6. This flood also re- 
sulted from a heavy winter snowfall. November, 1896, was 
a cold month, and the precipitation over the State averaged 
2.69 inches. This was greatly in excess of the normal. In 
December the precipitation was about normal, but in January, 
February and March, 1897, about 5 inches of snow fell, making 
a total winter precipitation of a little over 8 inches. The early 
part of March continued severely cold. Up to March 27, the 
day temperatures rose only slightly above freezing. Then a 
warm spell set in. From March 28 to 31, the day temperatures 
reached a maximum of from 50 to 55 degrees, and the night 
temperatures ranged from freezing to 6 degrees above. There 
was no precipitation during the last week of March, and the 
April precipitation was only half the normal. 

The temperature and precipitation on the watershed during 
both the spring of 1897 and 1916 are shown in Figs. 226 and 227. 

In 1916 conditions were favorable for a greater flood than 
in 1897, until the weather suddenly turned colder again the 
last days in March, making the break-up much more gradual 
than in 1897. Renewed warm weather and rains resulted in a 
secondary rise after April 20, 1916. 



Fig. 226. 




Mississippi River Watershed, Effect of Temperature and Pre- 
cipitation on Discharge at St. Paul, 1897. 



March 
10 20 




Fig. 227. — Mississippi River Watershed, Effect of Temperature and Pre- 
(334) cipitation on Discharge at St. Paul, 1916. 



RUNOFF . 335 

The Red River of the North at Grand Forks. — The Red 
River of the North drains an area of 25,000 square miles, most 
of which is prairie land with flat slopes and heavy soil.* The 
fall from the international boundary to Lake Winnipeg averages 
about six feet to the mile. This is much greater than the fall 
south of the boundary. From Lake Traverse to Lake Winnipeg, 
a distance of 315 miles, the entire fall is only 260 feet; 

A reasonably good record is available of the floods on the 
Red River, since 1800. The first great flood of which there is 
any record is that of 1826, when the river is reported to have 
risen 66 feet above low water. Snow fell in Pembina on October 
15, 1825, and remained on the ground throughout the succeeding 
cold winter, resulting in a spring flood. The next great flood 
occurred in 1852 when the gage reached 67 feet above low water. 

The greatest flood regarding which there is reliable information 
occurred in 1897. It began in the upper reaches on Apr.l 
1, and crested at Moorhead, April 5, and at the international 
boundary about three weeks later. A stage of 50.2 was reached 
at Grand Forks on April 10. There was no rain during the last 
week of March and the April precipitation was only half the 
normal. The flood resulted entirely from the melting of a heavy 
winter snowfall. During this flood, a strip of country about 
30 miles in width and 150 miles in length, was inundated, and 
about 50,000 people were rendered homeless. 

The temperature and precipitation on the watershed during 
both the 1897 and the 1916 floods are shown in Figs. 228 and 229. 

The cold weather during the first week of April, 1916, affected 
the runoff from the Red River watershed, at Grand Forks, 
in a similar manner to that from the Mississippi. If the rains 
between April 15 and 20 had come ten days earlier, or the 
weather had even continued warm, record-breaking floods would 
have occurred on both the Red and the Mississippi Rivers in 1916. 

Mass Curves of Temperatures Above Freezing. — Figs. 
230 to 234 show a summation of temperatures above freezing, 

* See "The Red River of the North" by E. F. Chandler, in The Quarterly 
Journal, TJniv. of N. D., April, 1911. 



March 

10 20 




Fig. 228. 



Red River Watershed, Effect of Temperature and Precipitation 
on Stage at Grand Forks, 1897. 



March 
10 20 




Fig. 229. 

(336) 



Red River Watershed, Effect of Temperature and Precipitation 
on Stage at Grand Forks, 1916. 



RUNOFF 



337 



with a view to illustrating the effect of spring temperatures 
on the flow of streams, in another manner. The break-up 
was much more nearly simultaneous over the entire state of 
Minnesota in 1897 than in 1916. While ordinarily the Min- 
nesota River breaks up before the Mississippi, bringing its 
flood water to the mouth, at St. Paul, before that from the north- 
ern part of the State arrives, in 1897 both streams crested at 
almost the same time. It appears that any one of three con- 
ditions would have produced greater floods in the Mississippi 
River at St. Paul, in 1916, than actually occurred: | 

1. More nearly uniform temperature conditions, as in 1897. 

2. Continued warm weather for five days longer. 

3. Moderately heavy rains ten days earlier. 

Figs. 230 to 234 give an interesting indication of the amount 
of warm weather required, in spring, to bring northern streams 
to flood stage. In 1897, the Mississippi River crested on April 
3, when the total number of degree-days of maximum daily 
temperature above 32° F. aggregated 170. In 1916 the crest 
occurred on April 6 at 175 degree-days. 



























































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MASS CURVES 

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338 



ELEMENTS OF HYDROLOGY 





































































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March April 

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Fig. 231b. 



RUNOFF 



339 



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MASS CURVES OF 

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Fig. 232. 



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MASS CURVES 

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Marcb 1897 April 

Fig. 233. 



340 



ELEMENTS OF HYDROLOGY 



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25 27 28 1 2 3 4 6 7 8 9 10 11 12 13 11 16 16 17 18 19 20 21 22 23 21 25 26 27 18 29 30 31 1 2 S 

Feb. March April 

Fig. 234. 

The Minnesota River crested at 1G5 in 1916. No record of 
crest is available for 1897. In 1902 the Ohio River crested, 
at Pittsburgh, at 150 degree-days. The Crow Wing crested 
at 165 in 1897, and at 172 in 1916. The Root River reached its 
highest at 95 in 1910 although there really was no crest at all. 
High water extended over the entire period from 80 to 175 degree- 
days. In 1913, the Root River crested at 135. Cold weather 
resulted in a rapid drop in stage with a second crest at 175. 
Then, another spell of cold weather set in and a third crest oc- 
curred at 195. In 1916 the first crest on the Root River oc- 
curred at 50 and a second and equal crest at 155. Neither crest 
was caused by rain. 

Both the Red River and the Little Fork streams, flowing 
north, crested much later, in 1916, than the streams flowing 
south. The Little Fork crested at 375 and the Red, a much 
larger stream, at 345. The forests on the Little Fork River 
watershed unquestionably retarded the melting of snow and 
contributed materially to the late crest. The Red River water- 
shed is from one-half to two-thirds prairie land. 

In 1897 the temperature rise was rapid, continuous and 



RUNOFF 341 

almost simultaneous over the Northwest and the Red River 
of the North crested at 215. 

It is also interesting to note that the crest of the Ohio River 
flood at Pittsburgh on March 1, 1902, occurred before the weather 
turned colder again, so that the full effect of the melting of the 
snow, combined with the rain, was felt. In case of the Root 
River, Minnesota, floods of March, 1913 and 1916, on the other 
hand, the crest was considerably lower than it would have been 
if warm weather had prevailed a few days longer. 

Fall Floods 

Many streams draining watersheds on which the summer and 
fall precipitation is heavy, are subject to fall floods. The 
Passaic River, N. J., flood of October 8, 1903, is a typical fall 
flood, and the greatest recorded for the stream. The Passaic 
River drains a steeply sloping, hilly fan-shaped area of 772 
square miles above Patterson, N. J. The flood was caused by 
a 30-hour rainstorm which averaged a precipitation of between 
10 and 12 inches. 

Many streams in the upper Mississippi Valley are subject 
to late summer and fall floods. A typical example is the October, 
1911, flood on the Black River, Wisconsin. 

The occurrence of summer and fall floods on streams greatly 
complicates the problem of the storage of water for combined 
power, navigation, and flood prevention purposes. This subject 
will be discussed in a later chapter. 

Flood Flow Formulas 

A large number of formulas have been prepared for the purpose 
of computing the probable flood flow from watersheds of various 
sizes. One group of formulas, including such well-known ones 
as McMath's, Hawksley's, Biirkli-Ziegler's, Adams', Hering 
and Gregory's and Parmley's, are intended, primarily, for use 
in sewer design and are applicable, particularly, to small areas 



342 ELEMENTS OF HYDROLOGY 

of less than one or two thousand acres. Other formulas, such 
as Kuichling's, Murphy's, Metcalf & Eddy's, and Fuller's, 
are applicable to the larger drainage areas. For a detailed 
discussion of these and other formulas, the reader is referred 
to books on sewerage. A discussion of some of the principles 
involved is, however, within the scope of this treatise. - 

Weight Given to Various Factors by Different Formulas. — 
Most of the formulas of that group applicable to sewer design 
assume the runoff in cubic feet per second to vary as the rate 
of rainfall in inches per hour, approximately as the .25 power 
of the slope of the ground, and approximately as the .8 power 
of the drainage area. The proportion of the rainfall reaching 
the sewers, dependent upon the character of the watershed, 
is usually expressed in a coefficient. Kuichling * concluded that, 

theoretically, the fourth root of the factor was the 

area 

proper one to use. 

Of the group of formulas applicable to estimates of flood flows 
from larger drainage areas, Kuichling's, Murphy's, and Metcalf 
& Eddy's assume only one variable, namely, the area of the 
watershed. The magnitude of floods, with respect to the inter- 
val of successive occurrences, is expressed in the coefficient 
used. Floods are grouped as "frequent," "occasional," "rare," 
"maximum," etc. The relation of watershed area to flood 
flow in second-feet per square mile, according to these formulas, 
is shown in Fig. 235. 

Fuller Formulas. — Fuller f introduces another variable into 
his formula, namely, the interval of time within which floods 
of a given magnitude are likely to recur. 

Watershed characteristics are taken care of, as far as pos- 
sible, by a coefficient. Fuller's relation between the size of 
drainage basin and ratio of maximum flood to average 24-hour 
flood is shown in Table 38. 

* Kuichling, Emil, Trans. Assoc. C. E., Cornell University, 1893. 

t Fuller, Weston E., Trans. Am. Soc. C. E., Vol. LXXVII, p. 564, 1914. 



RUNOFF 



343 




1000 2000 



3000 4000 5000 6000 ,7000 8000 9000 10000 
Watershed Area-Square Miles 

Fig. 235. 



344 



ELEMENTS OF HYDROLOGY 



TABLE 38. — RELATION BETWEEN MAXIMUM FLOOD AND 
AVERAGE 24-HOUR FLOOD (Fuller) 

Q (max.) = Q (1+2 A-*- 3 ) 



Catchment area, in 


Ratio of maximum 


Catchment area, in 


Ratio of maximum 


square miles 


flood to average 


square miles 


flood to average 




24-hour flood 




24-hour flood 


(1) 


(2) 


(1) 


(2) 


0.1 


5.0 


500 


1.31 


1.0 


3.0 


1,000 


1.25 


5.Q 


2.23 


5,000 


1.15 


10.0 


2.0 


10,000 


1.12 


50.0 


1.62 


50,000 


1.08 


100.0 


1.5 


100,000 


1.06 



Fuller's relation between the flood to be expected in a given 
period of years and the average yearly flood is shown in Table 
39. 



TABLE 39. — RELATION BETWEEN FLOOD TO BE EXPECTED 

IN A SERIES OF YEARS AND THE AVERAGE YEARLY 

FLOOD (Fuller) 

Q=Q (ave.) (1+0.8 log T) 



Time, in years 

(1) 


Ratio of largest flood 
to average vearly flood 

(2) 


Time, in years 

(1) 


♦Ratio of largest flood 
to average yearly flood 

(2) 


1 

5 
10 
25 


1.00 
1.56 
1.80 
2.12 


50 

100 

500 

1000 


2.36 
2.60 
3.16 
3.40 



This table is based upon the conclusion that the greatest flood 
which is likely to occur in the period of T years will exceed 
the average annual flood by .8 log T times the average annual 
flood. 

The variation of the ratio of maximum flood flow, in cubic 
feet per second, to the average 24-hour flow, in cubic feet per 
.second, with size of drainage area, represents a physical reality, 
although the ratio is also largely dependent on the character- 
istics of the watershed. The statement of the magnitude of 
flood, measured by the average annual flood on the given water- 
shed, to be expected in a certain number of years, represents 



RUNOFF 345 

merely a " probability " based on average observed occurrences. 
The maximum flood of a century may occur within five years' 
records of stream flow, yet, according to the law of probabilities 
as applied by Fuller, the flood to be expected in a period of one 
hundred years would still exceed this observed maximum of a 
century by nearly 70 per cent. When meteorological and hydro- 
logical data are entirely wanting, so that the cause of floods 
on the given stream cannot be studied, the use of such formulas 
as Fuller's may be justifiable, in that they serve as a rough 
guide. 

The lack of reliance to be placed on a formula giving the 
probable frequency of floods is well illustrated by the 1913 
floods in the Ohio Valley and in northeastern United States. 

The Hudson River at Mechanicsville, N. Y., drains an area 
of 5400 square miles. Records extend back about a hundred 
years, although accurate data are not available for the early 
years. According to Horton * the average of the highest day's 
discharge for each year of the 26 years preceding 1914 was 
41,875 second-feet. The greatest flood previous to 1913 occur- 
red in the spring of 1869, when the peak reached 67,000 second- 
feet. The crest of the 1913 flood reached 113,500 second-feet. 
This flood was preceded by warm rains that had taken most 
of the frost out, saturated the ground, and exhausted substan- 
tially all natural lake and swamp storage. The streams were 
at a bankful stage but there was no accumulation of snow on 
the ground except in a small portion of the Adirondack forests. 
An average of 4| to 5 inches of rain fell on the upper Hudson 
River watershed on March 25, 26, and 27, on practically satu- 
rated soil. 

Flood Frequency. — The frequency of flood stages on the 
Ohio River at Pittsburgh and at Cincinnati is shown in Figs. 
236 and 237. By extending these curves an estimate can be 
made of the probable frequency of still greater floods which 
are likely to occur. Not much weight can be placed on such 
* Horton, Robert E., Engineering Record, 1913, Vol. 66, p. 399. 



346 



ELEMENTS OF HYDROLOGY 



estimates, however. Up to a frequency of one flood in 25 years, 
the curves should be quite reliable. 



36 



34 



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FREQUENCY OF FLOODS 

OHIO RIVER 

AT 

PITTSBURG, PA. 

1878-1010 






















jLL — 


d Stage 















10 15 20 35 30 

Frequency - Tears per Flood 

Fig. 236. 



35 



10 



74 



70 



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04 



50 

































































OV^ 








FREQUENCY OF FLOODS 

OHIO RIVER 

AT 

CINCINNATI, OHIO 

1861-1910 


























r^ 10 


)d Stage 



















SO 25 30 35 

Frequency -Years per Flood c 

Fig. 237. 



40 



30 



RUNOFF 



347 



Suggested Definition of " Normal." — Fig. 238 shows the 
frequency of river stages between extreme low water and extreme 
high water, at Cincinnati, for 50 years. In this connection it 
is interesting to consider what constitutes the " normal " stage 
of a stream or the " normal " annual, monthly, or daily precipi- 
tation at a given station. The definition of " normal " applicable 



m- 


71.1 in. 18 


Si 








































60 










































a 


a 












FREQUENCY OF RIVER STAGES 












OHIO RIVER 














AT 
























CINCINNATI, OHIO 




a 
S80 










18G0-1910 
























20 
























































-Normal 








10 










































ft 




















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30 40 50 00 70 80 

Frequency - Per cent of Total Time (50 yra.) 

Fig. 238. 



90 



10Q 



to such phenomena would seem to be that given by Webster, 
as follows: 

" The ordinary or usual condition, degree, quantity, 
or the like." 
According to this definition, the term " normal " river stage 
would mean that stage which prevails the greatest percentage of 
the time. Such a stage is represented by the point of inflection 
or change of curvature on the frequency curve, and represents 
a very much lower stage than the mean, or average. 



348 ELEMENTS OF HYDROLOGY 

DATA RELATING TO SOME OF THE MOST SEVERE FLOODS 
Summer Floods on Small Watersheds 

Cane Creek, N. C, Flood. — Cane Creek has a slope of about 
150 feet per mile, and drains an area of about 22 square miles 
of rough, mountainous country, with much bare rock and, on 
the whole, very thin soil cover. The slope of the stream bed 
is so steep that the ordinary flood rise at Bakersville is only 
about five to six feet. During the flood of May, 1901, however, 
there was a rise of twelve feet. The flood plain of about 250 
acres of high-grade agricultural land lying just above the town 
was swept clear of soil down to the rock. Boulders from four 
to twenty tons in weight were moved from 100 to 300 feet. 

The precipitation which caused this flood amounted to about 
eight inches in 24 hours, resulting in a discharge estimated at 
29,500 c.f.s. or 1341 c.f.s. per square mile. 

In a number of places on the watershed there occurred what 
are locally known as " water spouts." Percolating water satu- 
rated the soil overlying the rocks, and when sufficient head 
had accumulated the water burst out, carrying earth, trees, 
etc., with it, and cutting great gashes down the hillsides. 

Heppner, Oregon, Flood. — The Heppner, Oregon, flood 
occurred on June 14, 1903, on a small watershed of about 20 
square miles, tributary to Willow Creek, in Oregon. The slope 
of the creek below Heppner is about 35 to 40 feet per mile. 
The flood was caused by excessive precipitation which lasted 
only about one-half hour. The storm area was about two to 
four miles in width and eight to ten miles in length. Such 
tremendous quantities of hail fell during the storm that five 
days later bodies were found well preserved in drifts of hail. 
Although there is no record of the exact size of the largest hail- 
stones, some were found in the debris after five days which meas- 
ured five-eighths inch in diameter. The hail was of a clear, 
practically transparent, ice. 

The flood crest appeared at Heppner almost coincidently 



RUNOFF 349 

with the first water and the creek was normal again in about 
1^ hours. The flood apparently traveled at a rate of about 
six miles per hour. One third of the town was entirely swept 
away, and out of a population of 1400, about 200 were drowned. 

Monterey, Mexico, Flood. — Throughout the arid and semi- 
arid region, torrential rains over small areas are the cause of 
most extreme and disastrous floods on small streams. The 
worst flood on record, of this character, is that which occurred 
at Monterey, Mexico, on August 27, 1909. This flood occurred 
on the Santa Catarina River, which is dry about 350 days out 
of the year. The river drains a fan-shaped area of 544 square 
miles, varying in elevation from 7,820 feet in the headwaters 
to 1,766 feet in the city of Monterey. Most of the watershed 
is rocky, barren, precipitous, and free from plant growth of all 
kinds. 

During August, 1909, two great floods occurred on this water- 
shed, as the result of excessive precipitation. The first and 
smaller flood occurred between August 9 and 10. It was never- 
theless the greatest flood since 1881. This flood followed the 
greatest drought in 30 years. From January, 1909, to August 
9 of that year, only eight inches of rain had fallen, and during 
the previous year the entire precipitation had amounted to only 
ten inches. During the flood of August 9 to 11, 13.38 inches of 
rain fell in 42 hours. From midnight to noon, August 10, 3.50 
inches fell; from noon on the tenth to 8 a.m. on the eleventh, 
7.11 inches; from 8 a.m. to 6 p.m. on the eleventh, 2.77 inches; 
or a total of 13.38 inches in 42 hours. Of this, 10.61 inches 
fell in 30 hours. The result was a flood that would have been 
considered record-breaking had it not so soon been followed 
by a still greater one. Notwithstanding the heavy precipitation 
and the heavy runoff during this first flood of August 10 to 
11, the river was dry again a few days later. 

The flood of August 10 was followed by 21.61 inches of rain 
in 98 hours from 4 p.m. August 25 to 6 p.m. August 29. 
The distribution of this precipitation between August 25 and 



350 



ELEMENTS OF HYDROLOGY 



29 is shown in Fig. 239. The crest of the flood occurred 
at 11 p.m. on August 27 after substantially 10 inches of rain 
had fallen at Monterey. It is probable, however, that the 
record of precipitation in the valley at Monterey is not a cor- 
rect measure of the precipitation over the headwaters of the 
stream. Otherwise, the flood crest should have occurred about 
noon on August 28, after over 15 inches of rain had fallen. 



25 



•S20 



■Sis 



no 



* 5 

























Ores 


of Flood 



























25 



27 26 

August, 1909 



29 



Fig. 239. — Precipitation during flood at Monterey, Mexico, 
on August 27, 1909. 



The normal August precipitation at Monterey is 3.54 inches, 
and the normal for September is 4.28 inches. The mean annual 
precipitation for 21 years was 19.86 inches, yet, in the one 
month of August, 1909, 34.99 inches of rain fell. 

The maximum discharge was estimated by Conway * as 271,- 
500 c.f.s. or 590 second-feet per square mile. On a small ad- 
joining watershed of 3| square miles, the observed runoff was 
2900 c.f.s. or 825 c.f.s. per square mile. 

During thi§ flood, 452 acres of the city of Monterey, Mexico, 
were completely destroyed and about 5000 lives lost. Consider- 
able flood damage also occurred in other parts of Mexico during 
August and September, 1909. 

* Conway, G. R., Engineering News, September 23, 1909, Vol. 62, p. 315. 



RUNOFF 351 

Winter and Spring Floods on Large Streams 

Lower Mississippi River Floods. — The total watershed 
area drained by the Mississippi River system, shown in Fig. 
240, is 1,240,050 square miles. The area above St. Louis is 
165,900 square miles. The Missouri River drains an area of 
527,150 square miles; the Ohio 201,700 square miles; and the 
Arkansas drains 186,300 square miles. 

While the drainage area of the Ohio River is less than four 
tenths that of the Missouri River, the precipitation over the 
Ohio River watershed is so much greater than that over the 
Missouri as to result in a maximum flood discharge of 1,400,000 
second-feet from the Ohio River as against 900,000 second-feet 
from the Missouri. The flood discharge of the Arkansas and 
the upper Mississippi above St. Louis amounts to 450,000 
second-feet each, and that from the Red River to 220,000. 

The distance, by river, from the source of the Mississippi in 
Lake Itasca, Minnesota, to its mouth in the Gulf of Mexico, 
is 2446 miles.*. 

The distance from the headwaters of the Missouri to the Gulf 
is still greater. On account of these great distances which the 
water must travel, and the great area of the watershed tributary 
to the main stream, excessive local rains have no effect on the 
floods of the lower Mississippi, except, perhaps locally, for a 
few hours, as happened on May 10, 1912. As the river was 
just cresting at New Orleans in this case, 7 inches of rain forced 
the crest up about a foot for a few hours. 

The Rains Causing These Floods. — General rains extending 
over several weeks, at least, are required to produce great 
floods in the Mississippi between Cairo and New Orleans. 
Any one of the larger lower tributaries of the Mississippi is 
capable of producing a serious flood in all years of more than 
normal winter and spring precipitation, but the Ohio River 
is the principal flood-producing tributary. The effect of the 

* Annual Report, Chief of Engineers, U. S. Army, 1909, p. 2677. 



352 



ELEMENTS OF HYDROLOGY 




RUNOFF 353 

Ohio River is well shown by the fact that the maximum discharge 
of the Mississippi River, below the mouth of the Ohio, is 2,000,000 
second-feet, and below the mouth of the Red it is only 300,000 
more. 

The ordinary winter and spring precipitation in the Gulf 
region is usually ample to bring the lower river to an ordinary 
flood stage. If, under such conditions, several successive rain- 
storms, originating in the Southwest, pass over Texas and up 
the Ohio Valley, a serious flood will usually result on the lower 
Mississippi. As the upper Mississippi usually crests later than 
the Ohio, its principal effect is to prolong the floods on the lower 
reaches of the Mississippi. At New Orleans the flood crest 
is so flat as to show only about 1 foot variation in 30 days. 

Flood Damage. — Floods occur on the lower Mississippi 
with great frequency, the average being about one every six 
years. In general, flood frequency increases with watershed 
area, although shape of area and other conditions frequently 
nullify the usual relationship. The duration of the flood stages 
on the lower Mississippi is from 30 to 60 days, and as the flood 
crest is usually reached late in the spring, the damage to agricul- 
tural lands is aggravated. As the flood crest occurs at contin- 
ually later dates between Cairo and the Gulf, and as spring 
occurs continually earlier with decreasing latitude, the inter- 
ference of flood water with agricultural pursuits becomes in- 
creasingly more important toward the South. 

Flood losses in the lower Mississippi and Ohio River valleys, 
in 1912, were estimated at over $75,000,000 and in 1913 at over 
$150,000,000. The area flooded between Cairo and the Gulf, 
in 1912, was about 12,000 square miles. The Federal Govern- 
ment fed 272,753 refugees and 50,000 cattle during the 1912 
flood. 352 miles of the St. Louis, Iron Mountain & Southern 
Ry. was under water — some of it for over five months. 

Ohio River Floods. — Floods of great magnitude, on the main 
water course of a large drainage basin, seldom result from sum- 
mer rainfall. Floods on the tributaries are not necessarily syn- 



354 ELEMENTS OF HYDROLOGY 

chronous with floods on the main stream. Excessive summer 
rains may produce extreme flood conditions on the minor tribu- 
taries of the Ohio River, but all the great floods on the main 
stream have been the result of winter or early spring precipitation 
or of a combination of both. 

The precipitation over the Ohio River valley occurs rather 
uniformly distributed through the year, averaging about 3^ 
inches per month. The winters are mild. The mean monthly 
temperature over the greater portion of the watershed ranges 
from about 25 to 35 degrees, and the mean annual temperature 
from 50 to 60 degrees. Sufficient snow accumulates, however, 
when the winter months are colder than usual, to be an important 
factor, in conjunction with heavy spring rains, in producing 
flood stages in the streams. 

The Ohio valley lies almost directly in the path of, or on the 
side of heaviest precipitation of, most of the cyclonic storms 
which cross the country from the West and pass out by way 
of the St. Lawrence River valley. A fortunate circumstance, 
which somewhat reduces the height of floods on the main stream 
and certainly reduces the frequency of serious floods, is the fact 
that the river flows in the opposite direction to that traversed 
by the storms which bring precipitation to this basin. (No 
alarm need be felt that these storms will ever become reversed 
in direction!) This permits a large portion of the discharge 
from the lower tributaries to get away before that from the 
upper tributaries arrives in the lower reaches of the stream. 

Comparative Flood Hydrographs. — None of the great Ohio 
River floods of the past set the high-water mark along the entire 
length of the river from Pittsburgh to Cairo. The 1913 crest 
set a new mark from St. Marys to Maysville and also from 
Mt. Vernon to Cairo. The 1884 flood still holds the record at 
Wheeling, Cincinnati, Louisville and Henderson. Comparative 
flood hydrographs for the Ohio River and its principal tributaries, 
for the floods of 1884, 1907 and 1913, are shown in Fig. 241. The 
gage height corresponding to flood stage is shown by a heavy line. 



355 

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COMPARATIVE FLOOD HYDROGRAPHS 

OHIO RIVER AND PRINCIPAL TRIBUTARIES 
1913 FLOOD ____— 



RUNOFF 355 

Flood of 1884. — The flood of February 4 to 15, 1884, was 
caused by the combination of heavy rain and melting snow. 
January, 1884, was cold, and heavy snow fell in the mountains. 
The ground was frozen over a large portion of the upper watershed 
when the warm spell set in. This caused the river to reach 
virtually flood stage before the rains began. An average of 
only three to five inches of rain fell over the watershed during 
the eleven days from February 4 to 14. The accumulated 
snowfall, however, rapidly melted when the temperature rose 
to about 60' degrees on February 5. Melting snow, combined 
with the moderately heavy precipitation, produced record 
flood stages on portions of the main stream. The large quan- 
tity of water delivered by the 1884 flood is well shown by the 
hydrographs of Fig. 241. 

Floods of 1913. — The floods of March, 1913, resulted, pri- 
marily, from excessively heavy, uniformly distributed precipita- 
tion over almost the entire watershed. There was practically 
no frost in the ground anywhere on the watershed, but the soil 
was pretty well saturated. The precipitation over the entire 
watershed of 203,000 square miles, between March 23 and 27, 
averaging 4.86 inches, is shown in Fig. 220. Two storms from 
the Southwest followed each other so rapidly as to practically 
become one. The path taken by these storms is indicated by 
the elongated area of equal rainfall shown in Fig. 220. 

The time interval involved in the passage of the storm up 
the valley is well illustrated by the profile of the water surfaces 
of the Ohio River, on March 25 and 27, Fig. 242. This figure 
also shows the flood crests at various points on the main stream 
and on its most important tributaries. 

The Great Miami River crested at Hamilton early on the 
twenty-sixth. The Scioto crested at Chillicothe about noon of 
the twenty-sixth and discharged its flood water into the Ohio, 
at Portsmouth, about a day later. The Allegheny, the Musk- 
ingum, and the Licking crested on the twenty-seventh. The 
Monongahela, the Kanawha, the Big Sandy, the Kentucky, and 



356 



ELEMENTS OF HYDROLOGY 



the Cumberland crested on the twenty-eighth, while the main 
stream at Cairo did not crest until April 4. 

The effect of the passage of the rainstorm up the valley is 
well shown by the fact that the Great Miami" caused a rise on 
the Ohio, 21 miles above the mouth of the Miami, at Cincinnati, 
to nearly flood stage, before the Ohio at Portsmouth, at the 
mouth of the Scioto, had barely started to rise. 



800 




29 



184 



264 317 355 407 408 604 

Distance below Pittsburgh - Miles 

Fig. 242. 



787 823 



924. 967 



The profile of water surfaces, Fig. 242, shows that the water 
level in the Ohio, on the night of the twenty-fifth, was higher 
at Cincinnati than at Maysville, sixty-one miles up river. 
Under these conditions the current, of course, was upstream or 
negligible, and the river channel acted as a reservoir. This 
condition prevailed for about thirty-six hours. 

The rapid rise of the Ohio at Portsmouth on the twenty- 
seventh was caused by the discharge from the Scioto. 

Seine River, Paris, Flood. — The flood on the Seine River 
at Paris, France, in February, 1910, was the second greatest 
flood in the history of this stream, which dates back over 250 
years. The area of the watershed is 30,370 square miles, and 
the flood discharge was about 83,500 second-feet. The river 



RUNOFF 357 

rose about 28 feet as the result of steady rains during December, 
January and February, amounting to about 8| inches, as against 
an average precipitation, during the same period, of about 4| 
inches. A large part of the January precipitation fell as snow, 
particularly in the mountains of the Yonne district. The 
ground was practically saturated and the water-table high. 
About January 15, a thaw and rain set in which quickly brought 
down a large portion of the accumulated snowfall. January 
21 to 22, a cold spell in the mountains temporarily held back 
what snow still remained. The crest of the flood came on Jan- 
uary 28, when the warm weather and rain brought the waters 
from the two main tributaries of the Seine to Paris at the same 
time. 

The greatest recorded flood on the Seine River occurred on 
March 1, 1658, when the stage rose to about 15 inches above 
the 1910 crest. The next greatest flood occurred in 1740 
when a maximum stage about 1| feet below the 1910 crest 
was reached. Between 1800 and 1900, eight floods occurred 
during which the stage rose within less than ten feet of the 1910 
crest. 

LOW-WATER FLOW OF STREAMS 

The low-water flow of streams, particularly where facilities 
for storage are absent, is at once the most important among 
stream-flow data and the most difficult to ascertain. On few 
streams of the country have records been taken sufficiently 
long to give a dependable value for low-water flow. By care- 
ful analysis, however, of the precipitation, temperature, and 
other conditions that surrounded the lowest recorded discharges, 
a reasonably good estimate of probable future extreme and 
ordinary low-water flow can be made. 

Effect of Precipitation. — A combination of hydrological 
conditions is usually the cause of low water, but deficient or 
ill-timed precipitation is the predominant one. On streams in 
the arid and semi-arid region, and also on many small streams 



358 ELEMENTS OF HYDROLOGY 

in other parts of the country, that are dependent upon surface 
runoff for their low-water supply, low discharge accompanies 
or immediately follows the period of deficient precipitation. 
On streams fed mainly by ground-water, on the other hand, 
the low-water flow is determined by the precipitation several 
months previous. Streams fed by melting snows are also de- 
pendent upon precipitation that fell long before the low-water 
stage is reached. The low discharge of these streams is also 
influenced by the rate of melting of the snow and the evapo- 
ration loss during the winter and spring. 

Effect of Ground-water Supply. — The low-water discharge 
of most streams in the United States consists of seepage flow 
derived from the ground-water supply. While this supply 
may be ample in early spring, its adequacy for the maintenance 
of a good low-water flow during the summer is dependent very 
largely upon the evaporation and transpiration draft upon 
ground-storage later in the season. This draft on storage 
is dependent, primarily, upon the depth to the water-table. 
If the level of saturation is about twenty feet below the surface 
of the ground in clay subsoils, and about ten feet in sandy 
subsoils, and if the watershed is free from matured forest cover, 
the ground-water supply is safe against evaporation and tran- 
spiration loss, and against the effects of deep freezing, and the 
low-water flow of the streams is dependent upon the amount 
of the ground-water supply at the beginning of the dry season 
and the character of the saturated subsoil. If the subsoil 
at the level of saturation is sand, the ground-water supply 
available for the maintenance of stream flow, for any given 
depth to the water-table, is from two to three times that 
which is available if the subsoil is clay. The best ground-water 
supply is found in regions of ample precipitation where both 
soil and subsoil are of fine, sandy character and forest cover 
is absent. 

Lake and Swamp Storage. — The extent to which, on a 
given precipitation, a natural lake will sustain stream flow 



RUNOFF 359 

during dry weather is dependent mainly upon its depth, as 
this determines its surface temperature and, consequently, 
the evaporation loss. This one factor usually quite over-shadows 
the effects of all others. However, a narrow outlet and small 
fluctuations in stage are usually indications of well-equalized 
outflow, but of relatively small, tributary drainage area. Large 
fluctuations in stage usually indicate a large tributary drainage 
area and a relatively narrow outlet. 

During dry weather, the evaporation loss- from all lakes is 
very high, and if a lake is shallow, the low-water outflow may be 
reduced to zero. Lake Milaca, at the headwaters of the Rum 
River in Minnesota, is an illustration of this condition. The 
watershed area above Onamia is 414 square miles, and the area 
of the lake is 207 square miles. The discharge from the lake 
during the 19 months from September, 1910, to March, 1912, 
following the hot, dry summer of 1910, amounted to only .21 
inch in depth on the drainage area, and during both winters 
the discharge was zero. Lakes Traverse and Bigstone, and Red 
Lake, in Minnesota, are other relatively shallow lakes with 
small tributary drainage basins, whose low-water discharge is 
zero or substantially that. 

Lake Superior, on the other hand, although it has a small trib- 
utary watershed, has such great depth that the temperature re- 
mains uniformly low throughout the year, with consequent reduc- 
tion in evaporation loss, and a well-sustained low-water outflow. 

Lakes located in the upper portion of a drainage basin usually 
have a small fluctuation in stage and are of much less benefit 
in equalizing stream flow than lakes in the lower portion 
of the basin. Ottertail Lake, in Minnesota, for example, lo- 
cated in the lower portion of the Ottertail watershed, though 
relatively small is, nevertheless, very effective in equalizing 
stream flow, although part of the equalization effected must 
be credited to the character of the tributary watershed. 

Lake storage is usually not as effective in maintaining low- 
water flow during protracted dry spells as ground storage, but 



360 ELEMENTS OF HYDROLOGY 

it is always much more effective than swamp storage — in 
fact, swamp storage is distinctly detrimental to low-water 
flow, even though swamps do equalize the ordinary runoff. 
This fact is well illustrated by the Thief River, Minnesota, 
which has a drainage area of 1010 square miles, above Thief 
River Falls. The discharge of this stream was zero for 5 months 
from October, 1910, to February, 1911, and aggregated only 
.12 inch in depth on the tributary watershed during the two 
years from September, 1910, to August, 1912. 

Effect of Temperature. — A sudden rise in temperature, in 
spring, sends most of the accumulated winter precipitation 
into the streams at once. A gradual rise permits much more 
percolation. Cold weather early in the fall, before snow has 
fallen, freezes the ground to such depths that later in the season, 
after the ground is covered with snow, the warmth of the earth 
underneath cannot thaw out the frozen ground, and hence 
winter percolation through the melting of snow from under- 
neath, is impossible, thus reducing the ground-water supply. 
High summer temperatures greatly increase evaporation and 
thus reduce percolation and ground-water supply. 

Low winter temperature, causing the formation of a heavy 
ice cover over streams and lakes, results in congealing a sub- 
stantial amount of water, aggregating ten to twenty per cent of 
the winter yield of small watersheds.* 

As the freezing often occurs very suddenly, six inches of 
ice cover forming in a few days, the reduction in daily dis- 
charge will be several times as great as the reduction in yield 
would indicate. 

The formation of ice cover over lakes does not reduce the 
low-water outflow so long as the point of control, at or near 
the outlet, remains free from ice cover, because the effective 
head of water on the control section remains unchanged, the 
weight of the ice being exactly equal to the weight of the water 
congealed. 

* See Hoyt, W. G., in U. S. G. S. Water Supply Paper, No. 337, p. 10. 



RUNOFF 361 

When the water-table is close to the surface of the ground, 
as in the case of marshes and swamps, low winter temperature 
combined with an absence of snow, results in freezing the ground 
to depths of several feet and thus imprisoning all ground-water 
contained in this layer. Moreover, even if no gravity-water 
is frozen up, the lowering of the temperature of the moisture 
in the soil results in an increase in the surface tension and 
consequently in the amount of moisture held by capillarity. 
This causes a lowering of the water-table through upward 
movement of capillary water. 

When the ground-water lies within the range of seasonal 
changes in ground temperature, winter weather will increase 
the viscosity of the water and reduce the rate of seepage flow 
by a substantial amount. 

When the ground-water lies far below the surface of the earth 
it is entirely free from the last two of these temperature effects 
and the yield of the watershed is determined, primarily, by the 
ground-water supply. Even under such conditions, however, 
the daily rate of discharge of the streams draining such water- 
sheds may be prominently affected by temperature changes. 
Some of the ground-water may be suddenly congealed in the 
river channels and the remainder may be retarded by the in- 
creased friction resulting from the ice cover. Of this remaining 
portion a substantial amount is stored in the river channel 
while the stage is being raised sufficiently to permit the flow 
of ground-water to be carried away through the increased cross- 
section necessitated by the increased friction resulting from 
ice cover. The effect of these temporary abstractions from 
stream flow is well illustrated by the data for the upper Missis- 
sippi River at Minneapolis, Fig. 243. About two inches of 
rain between November 23 and 28 had resulted in an increase 
of about 4000 second-feet in discharge. Before much of this 
rainfall had run off, however, a cold spell set in which sent the 
minimum temperature below zero. The result was a drop 
in discharge from 12,000 second-feet to less than 5000. This 



362 ELEMENTS OF HYDROLOGY 

was followed by a recovery to more than normal, indicating 
that not all of the November rain had had an opportunity to 
run off before the cold spell had set in. In November, 1906, 
moderately cold weather resulted in a reduction in discharge 
from about 11,500 second-feet to about 7000 second-feet. 
Warmer weather, with the minimum above freezing for two 
days, resulted in an increase in discharge to 10,500 second-feet. 
A return of cold weather was followed by a gradual re- 
duction in discharge to about 8500 second-feet, when a cold 
wave, the first week in December, quickly sent the discharge 
down to less than 5000 second-feet. The river gradually re- 
covered from this drop, and succeeding extremely cold spells 
had no further serious effect. 

In 1909 the discharge increased until late November to 
about 7000 second-feet as the result of the melting of the heavy 
snowfall in the middle of the month. Then a cold wave that 
sent the mean temperature to about zero, reduced the dis- 
charge to 2500 second-feet. From this low mark the river 
gradually recovered and subsequent zero temperatures had 
little effect. 

These data clearly show that in the case of the Mississippi 
River above Minneapolis, the principal temperature effect 
on the low-water flow is that which results in channel storage 
of large quantities of water while the stage is being raised to 
permit the normal discharge under the increased friction re- 
sulting from the rapid formation of ice cover and frazil. The 
secondary effects, those accompanying the second and third 
cold spells after the last thawing weather, are due to the con- 
gealing of water as the ice cover thickens. Temperature effects 
on the ground-water itself are no doubt limited to minor por- 
tions of the watershed area. 

Observed Low-water Flows. — The most complete summary 
of low-water stream-flow data is that given by Kuichling in the 
New York State Barge Canal Report of 1901. These data 
are of some value in so far as the streams to which they 



RUNOFF 



363 



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Fig. 243. — Effect of Temperature on the Low-Water Flow of the 
Mississippi River at Minneapolis, Minn. 



364 ELEMENTS OF HYDROLOGY 

refer are concerned, but can seldom be used in estimating the 
low-water flow of other streams, even in the same locality, 
because the watershed characteristics are practically never 
identical. Moreover, unless the hydrological conditions sur- 
rounding the observed low-water flows of these streams are 
known, little dependence can be placed on the data as they are 
no indication of the frequency with which the given low flows 
will probably be equaled, or even much lower flows experienced. 

Valuable low-water stream-flow data for Minnesota streams, 
accompanied by pertinent, although somewhat incomplete, 
precipitation data, given by W. G. Hoyt in U. S. G. S. Water 
Supply Paper, No. 337, p. 14, are reproduced in Table 40. 

The summer low-water flow of 1910 was due to exceptionally 
low precipitation — probably the lowest in the southeastern 
part of the State since the low- water period of 1864. 

The winter low-water flow of 1911 to 1912 was caused by 
exceptionally low temperatures between Dec. 25, 1911, and 
Feb. 12, 1912, and deficient ground-water supply. The maxi- 
mum temperature was below zero for 21 days during this 
period. Except for the fall precipitation being above normal 
the winter flow would undoubtedly have been still less. This 
is indicated by the winter flow of 1912-13, which in some 
streams was still lower than that of the previous year, because 
the fall precipitation was below normal even though the winter 
temperatures were about normal. 

In endeavoring to interpret the data of Table 40 the author 
found that the July and August, 1910, minimum flow was 
not necessarily the minimum flow resulting from the deficient 
1910 precipitation. On some streams the minimum occurred 
in the fall and winter of 1910, and on others the minimum of 
the summer of 1911 was actually less than the minimum of 
1910, notwithstanding greatly increased precipitation. This 
condition undoubtedly resulted from deficient ground-water 
supply. The author believes that low winter temperature 
cannot produce abnormally low flows on streams where the 



RUNOFF 



365 



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366 ELEMENTS OF HYDROLOGY 

water-table lies so far below the surface of the ground as it 
does in the Root River valley, Minn., for example. Ground 
temperatures do not change at this depth and low- water flow 
is determined by ground-water supply and not by temperature. 
On other streams, such as the Crow River where the water- 
table lies nearer to the surface, the low-water flow during the 
winter of 1910-11 was less than during the cold winter of 
1911-12, so that on this stream, too, the ground-water supply 
really seemed to be the controlling factor. 

It is not the intention, here, to say that temperature does 
not affect the flow of streams at all, because the thicker the ice 
cover, the more water is held back and the smaller the discharge. 
Relatively, however, this effect is far less than the effect of such 
differences in ground-water supply as commonly occur. The 
difference between the thickness of the ice that forms over streams 
in an average year and in an exceptionally cold year probably 
does not affect the winter yield of a watershed by more than 
5 per cent. The momentary effect of sudden cold spells, as in- 
dicated in Fig. 243, on the other hand, may reduce the flow 
to one-half or even one-third normal. 



CHAPTER X 
STREAM-FLOW DATA 

Need for Data. — The increasing utilization of the flow of 
streams for water power, water supply, sewage disposal, and 
irrigation purposes, and the disposition of excess water has 
created a great need for an accurate determination of the phys- 
ical quantities involved. The data required are not only 
the ordinary flow of a stream but its extremes of flow, and the 
variations in flow through the day, the month, the year, and 
through the cycle of dry and wet years. 

How Data are Obtained. — Stream-flow data may be obtained 
directly, by the measurement of flow, or indirectly by computing 
runoff from such physical data as rainfall, temperature, and 
watershed characteristics. So far as possible, the actual flow 
of streams should be instrumentally measured, but when the 
data secured through such measurements cover only a few years 
and do not include the extremes of meteorological phenom- 
ena to be expected on the given watershed, such measurements 
may advantageously be extended by computations of flow based 
on physical data. 

Current Meter Measurements 

The method everywhere acknowledged as best adapted to 

an accurate determination of the discharge of practically all 

streams is that of determining the velocity of the water by 

means of a current meter and the cross-sectional area of the 

channel by means of soundings. By determining the relation 

between the stage of a stream, or the "gage height," and the 

amount of water flowing, or the "discharge," by means of meter 

measurements at various stages, and by obtaining either a con- 

367 



368 ELEMENTS OF HYDROLOGY 

tinuous record, or frequent readings of the gage as circumstances 
may demand, a continuous record is secured of the- discharge 
of the stream. 

The Gaging Station. — The place on a stream at which gage 
heights are observed and where usually meter measurements 
are also made, is known as a "gaging station." The selection 
of a gaging station is one of the most important steps in obtain- 
ing accurate records of stream flow. 

The ideal gaging station should possess the following character- 
istics : 

1. It should be located just above a " point of control," 

that is, a place in the stream where the fall at all 
stages is greater than in the reaches just above and 
below. 

2. It should offer a conveniently located and secure, shel- 

tered spot for the gage and be readily accessible to 
the observer. 

3. The channel of the stream should be stable and per- 

manent, free from vegetation and not subject to 
overflow. 

If the reconnaissance for the gaging station is made at low 
water, a good point of control can be more readily identified 
than at high stages. Provided the channel is permanent, a place 
in the stream that constitutes a point of control at low stages 
will also be a control at high stages if the channel is narrower 
than in the reach below or if the fall at the control is quite 
large. 

On those smaller streams with continually shifting channel 
bed and banks, where the obtaining of accurate stream-flow 
records is essential, artificial controls must often be provided. 
These may consist of a concrete weir or a ridge of boulders 
carefully placed in the channel. 

The Meter Section. — The cross section of the stream at 
which the velocity is measured is known as the meter section. 
This section may be a considerable distance either up or down 



STREAM-FLOW DATA 369 

stream from the gaging station so long as no appreciable amount 
of water enters the stream in the intervening distance. It 
is not unusual for the meter section on a large stream to be 
located several miles from the gaging station. 

The ideal meter section should possess the following charac- 
teristics : 

1. The channel for some distance above and below the 

section should be reasonably straight and uniform in 
cross section, and the bed and banks should be 
smooth and regular. 

2. The velocity should be reasonably uniform from bank 

to bank, and the water should move as near to stream 
lines as possible. 

3. The mean velocity should, if possible, range somewhere 

between 2 and 6 feet per second. 

It is often desirable to use different meter sections at different 
stages, so that for each stage the requirements of the ideal 
section may be as nearly attained as possible. 

A permanent channel is not a necessity for the meter section 
although it is for the gaging station. 

If the bed and banks are permanent, however, which is the 
case if the meter section is at the gaging station, the cross sec- 
tion of the channel can be fully developed by sounding below 
the water line and by level above this line. In developing 
the cross section a permanent point known as the "initial point," 
to which all distances across the stream are referred, is first 
established. Thereafter, when making meterings, merely the 
elevation of the water surface need be determined to secure 
the depths at the points where the velocity is to be measured, 
and the area of cross section. 

Soundings in moderately deep water can best be made with 
a pole graduated to feet and tenths. For greater depths a 
weight attached to sash cord is satisfactory, although the pos- 
sibility of shrinkage and stretching must be kept in mind, 
For great depths and swift water a heavy weight suspended by 



370 ELEMENTS OF HYDROLOGY 

wire is necessary. On the Lake Survey, in sounding fifty- 
foot depths, a 136-pound weight was used. 

Distances on the cross section may be marked on the rail- 
ing, when measurements are made from a bridge, or by a tagged 
line stretched across the river when measurements are made 
from a boat, or a cable car, or by wading. In case floating 
logs or boats, or great width of channel make the use of a tagged 
line impracticable, distances on the section may be determined 
by observing angles to a base line on shore, by means of a sex- 
tant. Under such conditions, and also when the channel 
is shifting, soundings must be taken each time a measurement 
is made. The distance between soundings is determined by 
the size and character of the stream and may be 2, 5, 10, or 
20 feet. 

The Staff Gage. — The gage most commonly used in deter- 
mining the stage of the stream consists of a graduated scale 
from which the elevation of the water above an actual or an 
assumed datum is read directly. Such a gage may consist of a 
wooden staff painted and graduated into feet and tenths, or of 
a scale cut into masonry walls or piers, or of metal plates with 
figures enameled upon the face. The gage may be placed in 
either a vertical or an inclined position. 

The zero of all gages should be referred to at least two bench 
marks of permanent character, located in the immediate vi- 
cinity of the gage and should be instrumentally checked at least 
once a year. 

The Hook Gage. — The hook gage consists of an inverted, 
graduated rod with an upturned hook at the bottom. The 
rod slides in a groove to which a vernier may be attached for 
precise reading. This type of gage gives the most accurate 
determinations of water level but is used mainly in laboratory 
work. 

The Chain Gage. — The chain gage consists of a weight which 
is lowered by a chain until it touches the surface of the water. 
The weight generally hangs supported over a pulley, the chain 



STREAM-FLOW DATA 371 

being led horizontally over a graduated scale from which the 
readings are made. When placed out-of-doors, the chain, scale, 
and weight should be enclosed in a box. The length of the chain 
should be checked occasionally and necessary corrections applied 
to the readings. A chain gage may be advantageously used where 
logs, ice, or other floating debris would destroy a staff gage. 

The Automatic Recording Gage. — The advisability of in- 
stalling a recording gage depends, mainly, upon whether two 
or three readings of stage a day will be sufficient for obtaining 
the correct daily discharge of a stream. The conditions under 
which a continuous record of stage is often necessary and the 
installation of a recording gage desirable, are: 

1. Rapid fluctuation in stage due to changes in the amount 

of water used by power plants, to log sluicing, or to 
the operation of diversion works on. irrigation pro- 
jects. 

2. Rapid fluctuations in the stage of streams draining 

small watersheds, as the result of torrential rains or 
the sudden melting of snow. 

3. Inaccessibility of gaging station or unreliability of 

observer. 

4. Necessity for continuous records of flow for legal pur- 

poses. 

Diagram A in Fig. 244 well illustrates the daily fluctuations 
in stage due to variations in the amount of water used by power 
plants. Under such conditions continuous records of stage 
are clearly necessary for the accurate determination of daily 
discharge. 

Diagram B in Fig. 244 illustrates the reduced effect of power 
plant operation at medium and high stages when only a small 
portion of the stream flow is being utilized by the plant. 

Fig. 245 illustrates the large fluctuation in flow occurring 
within a few hours on many small streams. On such streams 
morning and evening gage readings, only, would introduce 
gross inaccuracies into the resulting daily discharge. 



372 



ELEMENTS OF HYDROLOGY 



J9&J in hiSisij aSi^o 






^T 

? r — ~^ 




.2 « 



a, 
O 



o * 
Ph .2 

t-l 



■* Ph 



fe cc 



STREAM-FLOW DATA 



373 




From U.S.G.S. Water. Supply Paper No. 375. 

Fig. 245. j — Rapid Fluctuations in Flow of Small Stream, North Fork of 
Wailua River Near Lihue, Kauai, Hawaii. 

Fig. 246 shows the principal types of recording gages in use. 
The essential mechanical features of these gages are a float, and 
a chain belt connected to the float at one end and to a weight 
at the other end and carried up over a sheave which actuates a 
recording device that traces or prints the height of the float 
on a clock-operated record sheet. 

The installation of a recording gage is well shown in Fig. 247. 
Staff gages for comparing the level of the water in the well 
with that in the river outside should always be installed, so 
that clogging of the intake may be immediately detected. The 
gage shelter should be well aired and camphor gum placed under 
the cover of the gage itself to help keep the record sheet dry. In 
cold weather a lamp or other heating device may be used to 
keep the gage from freezing up; or kerosene may be used 
in the float chamber, when this is not too large, and the difference 
in specific gravity between the kerosene and the water allowed 
for in gage reading. 



STREAM-FLOW DATA 



375 



Recording gages are built to run from one day to 30 days 
or more. The most common kind is the seven-day gage. 

As the discharge does not usually bear a straight line relation 
to the gage height, the mean daily gage height for a stream sub- 
ject to great fluctuations in stage does not give the mean daily 
discharge. This must be based upon the mean hourly dis- 
charge corresponding to the observed mean hourly gage height. 





From U.S.G.S. Water Supply Paper No. 384. 

Fig. 247. — Typical Recording Gage Installation. 



The Current Meter. — Although a considerable number of types 
of current meters have been used for measuring stream flow at 
various times in the past, the two in most common use today 
are the Price and the Haskell meters, illustrated in Figs. 248 
and 249. The essential parts of both types of meters are a 
wheel revolved by the flowing water and a mechanism that 
reports the revolutions of the wheel to the observer. 

The Haskell meter has a screw-propeller type of wheel 
mounted on a horizontal axis. The Price meter has a wheel 
consisting of several conical cups mounted on a vertical axis. 



376 



ELEMENTS OF HYDROLOGY 




Fig. 248. — Small Price Current Meter with Telephone Sounder, 
Cable and Battery. 




Fig. 249. — Haskell Current Meter and Register. 



STREAM -FLOW DATA 377 

A small form of Price meter is used almost exclusively by the 
United States Geological Survey. The Haskell meter is exten- 
sively used by other departments of the Government. Both 
meters yield good results. The Price meter is lighter but 
slightly over-registers in turbulent water. The Haskell meter 
is less affected by floating weeds or inner bark and very slightly 
under-registers in turbulent water. The characteristics of these 
two types of meters are fully discussed by Groat and others in 
Trans. Am. Soc. C. E., Vol. LXXVI, 1913, pp. 819 to 870. 

To obtain good results, the current meter should receive the 
same care that is accorded any delicate piece of mechanism. 

Rating the Meter. — In order to obtain the actual velocity 
of the moving water, the relation between revolutions of meter 
and velocity of water, through widely varying limits, must be 
known, that is, the meter must be rated. 

The rating of the meter consists in moving it through still 
water, at various speeds, over a course of known length, and 
recording the number of revolutions made by the meter and the 
time consumed in traveling over the course. 

The rating of the meter should be performed under as great 
a variety of conditions as is to be expected in the use to which 
the meter will be subjected. Relative to the need for uniform 
speed in rating, Shenehon * states : 

"It is not very important to traverse the base at a pre- 
cisely uniform speed, because the stream flow which the 
meters measure is not entirely uniform. It comes in pul- 
sations, sometimes lagging, sometimes spurting, and the 
uniformity in the rating speed need not be greater than 
that of the stream." 

For each rate of speed the meter should be run over the 
course in both directions so as to eliminate any wind or current 
effects. 

The applicability of a still-water rating to the measurement 
of flowing water has often been questioned. The U. S. Lake 
* Shenehon, Francis C, Minnesota Engineer, Vol. 17, No. 3, p. 123. 



378 



ELEMENTS OF HYDROLOGY 



Survey,* however, has proven by a series of carefully conducted 
experiments in 1906, that for velocities of about three feet per 
second, at least, the still-water rating gives absolutely correct 
results. 

A comparison of still-water and moving-water ratings made 
by the U. S. Geological Survey f shows that still-water ratings 
are correct for all velocities above one foot per second. 



TYPICAL RATING TABLE 



a 
o 

E 






. 




Yelocity 


n feet 


per second 


• 








6 



5 


10 


20 


30 


40 


50 


60 


70 


80 


90 


100 


150 


200 




s 
p. 


revs. 


reva. 


revs. 


revs. 


revs. 


revs. 


revs. 


revs. 


revs. 


revs. 


revs. 


revs. 


revs. 


40 


0.31 


0.58 


1.13 


1.68 


2.23 


2.78 


3.34 


3.90 


4.45 


5.01 


5.56 


8.34 


11.12 


40 


41 


0.30 


0.57 


1.10 


1.64 


2.18 


2.71 


3.26 


3.81 


4.34 


4.89 


5.43 


8.14 


10.85 


41 


42 


0.30 


0.56 


1.07 


1.60 


2.13 


2.65 


3.18 


3.72 


4.24 


4.77 


5.30 


7.95 


10.59 


42 


43 


0.29 


0.54 


1.05 


1.56 


2.08 


2.59 


3.11 


3.63 


4.14 


4.66 


5.18 


7.77 


10.34 


43 


44 


0.28 


0.53 


1.03 


1.53 


2.03 


2.53 


3.04 


3.55 


4.04 


4.55 


5.06 


7.59 


10.10 


44 


'45 


0.28 


0.52 


1.01 


1.50 


1.99 


2.48 


2.97 


3.47 


3.95 


4.45 


4.95 


7.42 


9.87 


45 


46 


0.28 


0.51 


99 


1.47 


1.95 


2.43 


2.90 


3.39 


3.87 


4.35 


4.84 


7.26 


9.65 


46 


47 


0.27 


0.50 


0.97 


1.44 


1.91 


2.38 


2.84 


3.32 


3.79 


4.26 


4.74 


7.11 


9.45 


47 


48 


0.26 


0.49 


0.95 


1.41 


1.87 


2 33 


2.78 


3.25 


3.71 


4.17 


4.64 


6.96 


9.25 


48 


49 


0.26 


0.48 


0.93 


1.38 


1.83 


2.28 


2.72 


3.18 


3.63 


4.09 


4.54 


6.81 


9.06 


49 


50 


0.26 


0.47 


0.91 


1.35 


1.79 


2.23 


2.67 


3.12 


3.56 


4.01 


4.45 


6.67 


8.89 


50 


51 


0.25 


0.46 


0.90 


1.32 


1.75 


2.19 


2.62 


3.06 


3.49 


3.93 


4.36 


6.54 


8.72 


51 


52 


0.25 


0.46 


0.88 


1.29 


1.72 


2.15 


2.57 


3.00 


3.42 


3.85 


4.28 


6.42 


8.56 


52 


53 


0.24 


0.45 


0.86 


1.27 


1.69 


2.11 


2.52 


2.94 


3.36 


3.78 


4.20 


6 30 


8 40 


53 


54 


0.24 


0.44 


0.85 


1.25 


1.66 


2.07 


2.47 


2.88 


3.30 


3.71 


4.12 


6.18 


8.24 


54 


55 


0.24 


0.43 


0.83 


1.23 


1.63 


2.03 


2 43 


2.83 


3.24 


3.64 


4.05 


6 07 


8.09 


55 


56 


0.23 


0.43 


0.82 


1.21 


1.60 


1.99 


2.39 


2.78 


3.18 


3.58 


3.98 


5.96 


7.95 


56 


57 


0.23 


0.42 


0.80 


1.19 


1.57 


1.96 


2.35 


2.73 


3.12 


3.52 


3.91 


5.86 


7.81 


57 


58 


0.22 


0.41 


0.79 


1.17 


1.54 


1.93 


2.31 


2.68 


3.07 


3 46 


3.84 


5.76 


7.68 


58 . 


59 


0.22 


0.41 


0.78 


1.15 


1.51 


1.90 


2.27 


2.63 


3.02 


3.40 


3.77 


5.66 


7.55 


59 


60 


0:22 


0.40 


0.77 


1.13 


1.48 


1.87 


2.23 


2.59 


2.97 


3 34 


3.71 


5.56 


7.42 


60 


61 


0.22 


39 


75 


1 11 


1.46 


1.84 


2.19 


2.55 


2.92 


3.29 


3.65 


5.47 


7.30 


61 


62 


0.21 


39 


0.74 


1.09 


1.44 


1.81 


2.16 


2.51 


2.87 


3.24 


3.59 


5.38 


7.18 


62 


63 


0.21 


38 


0.73 


1.07 


1.42 


1.78 


2.13 


2.47 


2.82 


3.19 


3.53 


5.30 


7.07 


63 


64 


0.21 


0.38 


0.72 


1.05 


1.40 


1.75 


2.10 


2.43 


2.77 


3.14 


3.48 


5.22 


6.96 


64 


65 


0.20 


0.37 


0.71 


1.03 


1.38 


1.72 


2.07 


2.39 


2.73 


3.09 


3.43 


5.14 


6.85 


65 


66 


0.20 


0.37 


0.70 


1.02 


1.36 


1.69 


2.04 


2.35 


2.69 


3.04 


3.38 


5.06 


6.75 


66 


67 


0.20 


0.36 


0.69 


1.01 


1.34 


1.66 


2.01 


2.32 


2.65 


2.99 


3.33 


4.98 


6.65 


67 


68 


0.20 


0.36 


0.68 


1.00 


1.32 


1.64 


1.98 


2.29 


2.61 


2.95 


3.28 


4.91 


6.55 


68 


69 


0.19 


0.35 


0.67 


0.99 


1.30 


1.62 


1.95 


2.26 


2.57 


2.91 


3.23 


4.84 


6.45 


69 


70 


0.19 


0.35 


0.66 


0.98 


1.28 


1.60 


1.92 


2.23 


2.53 


2.87 


3.18 


4.77 


6.36 


70 



A good rating can be secured by sending- the meter to the 
United States Bureau of Standards at Washington, which does 
the work for a small charge. The rating furnished by the 
manufacturer is usually correct to about two per cent. 

* Shenehon, Francis C., Minnesota Engineer, Vol. 17, No. 3, p. 123. 
t Water Supply and Irrigation Paper, No. 95. 



STREAM-FLOW DATA 



379 



From the rating just described, tables are prepared giving 
the relation between the number of revolutions of the meter 
in various periods of time, and the corresponding velocity of 
the water. A typical rating table is shown on p. 378. 

The Mean Velocity. — The discharge of a stream represents 
the product of its cross-sectional area times its mean velocity. 
The area can be ascertained by soundings but the mean velocity 




0.20 



1.20 



0.40 0.60 0.80 1.00 

Velocity in Terms of Mean Velocity =1.00 

Mean of 78 curves without ice cover 

Mean of 42 curves with ice cover 

From U.S.G.S. Water Supply Paper No. 187. 

Fig. 250. — Typical Vertical Velocity Curves with and without Ice Cover. 

cannot be directly determined. It can only be computed after 
the discharge itself has been ascertained. This is done by sum- 
ming up the partial discharges in relatively small vertical sec- 
tions of the stream, determined by means of velocity measure- 
ments in the end verticals of the sections and the depths of water 
in these verticals, as derived from the soundings. The verticals 
in which velocity measurements are made may be 2, 5, 10, 20, 
or even 50 feet apart, depending mainly upon the width and 
depth of the stream and the uniformity of the flow. 



380 



ELEMENTS OF HYDROLOGY 



Fig. 250 shows typical vertical velocity curves. A study of 
a large number of similar curves has resulted in establishing 
as a practical fact that the mean velocity in a vertical, irre- 
spective of depth or character of stream, is found at a point 
approximately six-tenths of the depth below the water surface, 
and that the mean of the velocity at the two-tenths depth and 
at the eight-tenths depth will almost exactly equal the mean 
velocity. 

The point of maximum velocity generally lies between the 
surface and a point at one-third of the depth. The following 
table shows the relation between depths of maximum and mean 
velocity, measured from the surface down. 



Depth of point of 
maximum velocity 


Corresponding 

depth of point of 

mean velocity 




0.1 d 
O.lod 
0.20 d 
0.25 d 
0.30 d 
0.33 d 


0.58 d 
0.59 d 
0.60 d 
0.62d 
0.63 d 
0.65 d 
0.67 d 



d = total depth of water 

The usual velocity curve is a parabola with its axis horizontal 
through the point of maximum velocity. In such a curve 
the mean of the velocities at .21 and .79 of the depth below 
the surface theoretically gives the true mean velocity. Also, 
the mean of the velocities at .15, .50 and .85 depth gives the 
mean velocity in the vertical.* 

Evidently, the use of the average of the velocities at .2 and 
.8 depth, for the determination of the mean velocity in the 
vertical, is correct in theory, and it is also fully substantiated 
by a great many observations. 

When a high degree of accuracy is required in meter gaging, 
two meters may be used to advantage. One is held contin- 
ually at the .6 depth while the other is held successively at .2 
* Engineering News, Vol. 75, p. 889. 



STREAM-FLOW DATA 



381 



and .8 depth, or at each tenth depth in case vertical curves 
are to be plotted. The meter which measures the mean velocity 
directly at the .6 depth can be used to indicate changes in velocity 
due to the pulsations noticeable in the flow of nearly all streams. 
In shallow, turbulent, and hence rough-bedded streams, the 
measurements of velocity at .6 depth usually gives results that 
are less in error than when measurements at .2 and .8 depth 
are attempted. 




o 1.0 2.0 

Velocity- Feet per Second 

Fig. 251. — Typical Vertical Velocity Curves in Tailrace of Power Plant. 



In extremely swift water it may be impracticable to sink 
the meter far below the surface. Under such conditions meas- 
urements of velocity may be made at about half a foot below 
the surface and 85 per cent of these values taken as the approxi^ 
mate mean velocity in the vertical. 

In measuring velocity it is also possible to obtain the mean 
in the vertical by what is known as the integration method; 
i.e., by moving the meter through the entire depth at a uniform 
speed. The Price meter is not adapted for use with this methods 



382 ELEMENTS OF HYDROLOGY 

The Haskell meter gives correct results, as vertical motion has 
no effect on the wheel. 

In measuring the discharge through sluice gates and from 
turbines it is usually necessary to determine the velocity for 
each tenth of depth in the vertical, as the point of mean velocity 
does not always have its usual location on account of initial 
impulses received by the water. Typical vertical curves taken 
by the author in connection with power plant tests are shown 
in Fig. 251. 

Making the Measurement. — When the meter section is 
located at a bridge, the meter may be held over the edge of 
the roadway or the railing, or suspended from the end of a spar 
so as to get the meter beyond the influence of the pier-s. When 
meterings are made from a boat, the boat is kept in position 
by means of a wire or cable stretched across the stream, or by 
means of an anchor. When a cable is used, it may be marked to 
serve also as a tag line; and when the river must be kept open 
for boats or floating logs, the cable may be permitted to rest 
on the bottom except at the measuring point. When the use 
of a cable is impracticable, the position of the measuring point 
on the cross section may be determined by sextant, as previously 
indicated. 

On the smaller streams a cable and car can advantageously 
be used for making the measurement. Typical U. S. Geological 
Survey metering stations are shown in Figs. 252 to 255. 

The meter is held in position and the number of revolutions 
observed for from 40 to 70 seconds, at each .2 and .8 depth on 
each vertical, consecutively, across the stream. These verticals, 
as previously stated, may be from 2 to 50 feet apart, depending 
upon the character of the channel. The gage at both the 
gaging station and at the meter section — if these are not at 
the same place — should be read at the beginning and at the 
end of the metering to indicate changes in stage. 

The meter may be suspended from a cable with the aid of 
a weight or, in measuring small streams, it may be attached 




From U.S.G.S. Water Supply Paper No. 94. 

Fig. 252. — Making a Meter Measurement from a Boat. 




From U.S.G.S. Water Supply Paper No. 304. 

Fig. 253. — Making a Wading Measurement. 



(383) 



384 



ELEMENTS OF HYDROLOGY 



to the end of a rod. In deep, swift water a guy line may be 
necessary to keep the meter in the vertical; or the pull and 
angle of the cable at the observer's end may be recorded and 
the proper position of the meter computed. 




From U.S.G.S. Water Supply Paper No. 371. 

Fig. 254. — Making a Meter Measurement from a Cable Car. 



In deep, swift water the meter may also be suspended froi 
a piece of uninsulated piano wire or small cable and the circuit 
completed by dropping the observer's end of the wire, having 
a metal plate attached, into the water. This arrangement 
offers very little resistance to the flow of water and consequently 
keeps the meter in a very nearly vertical position. 



STREAM-FLOW DATA 



385 



The most common devices for determining the revolutions 
of the meter in a given time are the electrical register and the 
telephone receiver. The latter is light, which is of importance 
in wading measurements, but focuses the attention of the ob- 
server on the counting of the clicks of either single, fifth or 




From U.S.G.S. Water Supply Paper No. 304. 

Fig. 255. — Making a Meter Measurement from a Bridge. 



tenth revolutions, according to the device used in the meter, 
The electrical register is automatic and requires merely the 
starting and stopping of the mechanism and the reading of the 
number of revolutions and the time. A stop-watch is essential 
in accurate work. 

The Field and Office Notes. — Whenever a considerable 
amount of meter gaging is to be done, special notebooks or 



386 ELEMENTS OF HYDROLOGY 

loose-leaf blanks with proper printed column headings should 
be prepared and used in recording the field observations and 
also the results of the necessary office computations. Any un- 
usual circumstances surrounding the measurement should also 
be recorded in the notes for possible future use in the inter- 
pretation of irregularities in the observations. 

Two typical sheets from a set of field notes of a meter measure- 
ment are shown on the following pages. 

The Discharge Curve. — After meter measurements have 
been made through at least the principal range in stage on the 
given stream, a " discharge curve " (Fig. 256) is drawn on cross- 
section paper by plotting the metered discharges against the 
corresponding observed gage heights. With the smoothed 
curve drawn through the observed points as a basis, a table 
is prepared for office use, giving the discharge in cubic feet 
per second corresponding to each tenth or half tenth foot in 
gage height. Such a table for the Ottertail River is shown 
below. 

If possible, a field determination should be made of the gage 
height corresponding to zero flow. If the gaging station is 
located above a well-defined point of control, zero flow will 
correspond to the gage height that represents the elevation 
of the river bottom at the control. This can usually be deter- 
mined by soundings at the time the gaging station is established. 
The gage height corresponding to the stage of zero flow helps 
greatly in determining the low-water portion of the discharge 
curve. 

If the gaging station is established at a good point of control, 
and the discharge curve has once been well determined, a single 
metering a year, taken at the time the zero of the gage is checked, 
will usually give sufficient verification of the curve and hence 
of the stability of the control. 

In case the meter section is not at the gaging station the 
cross section of the stream at the gage should also be determined 
so that both area and mean velocity curves at the gage may 



STREAM-FLOW DATA 



387 



TYPICAL DISCHARGE MEASUREMENT NOTES 

No. of Meas ,.. 



Date jJmJa0....Zj(. , 191^ 

Width... 

Party &^J3>.£.q.</.{<&'!. Disch 

Staff gage, checked with-ievel and found 



.... R,ver « <3.e.K/T7.<?.n£b.i;^c./i state oi..M.mf3*.... 

Cfook near /^sr^us /^//.s 
^T. Area'..... ,£./<£ Mean Vd. ...*3.Z7. Cor. M. G. H. ZS8 



7/3 c.f.&. 



Chain length, checked with steel tape, 12-lb. pull, found /£•.<?*?...... ft. 

" "/^changed to.n.. t .. w ..i.jfti at...,. i u...,i.o'ilooli > Correct length /.§.:&&.. ft. 

" "• corrected on basis of levels to .....ft. at o'clock. 



Gage reading 
....g : .^0 



.&#€. 



Time 



ZJBCJSM. 



Station 



„.4/fejr. 



Meter No..; &//..•&./!?... 

Date rated. M.<?.X..g4../3/£ 

Meas.beganj^/fiVtf ; ended.£££.^*?L 
Time of meas. (hrs)/.g5"...Method./~..<^?t 

No. meas. sec*s'...v?.^ Coef../.££. ....... 

Av. width sec. ../•.•?..,.... Av. depth..v?:."£... 

G. Ht. change (total.) :.<?<?. 

...£.&...% diff.by...^/jf^f..rating table. 



Weighted mean G. Ht &.'&&.. ft. 

Correct " " " £.■£§... ft. 

Meas. from -eabl*) bridge, bo a t, w adi ng . Meas. at f t . nbo y e, .below gage. 

If not at regular section note location and conditions ■. 

.....Area from soundings (date). Z/7<«£. .<??7<Z<$$i.... 

Method of suspensioni*Wf7«»5<JW'/7.<<a , WStay wire Approx. dist. to W. S. .../P.. 

Arrangement of weights and meter; top hole ; middle holt.. /I?....; bottom hole..6r!..... 

Gage inspected, found C?j/£: Cable inspected, found .... 

Distance apart of measuring points verified with steel tape and found „ 

Wind fXff.tfif: upctr < t downotn, aoroooi Angle of current /x?./^{?7.{?.<. 

Observer seen /?/.$. G. Ht. book inspected /Yff. 

Examine station locality and report any abnormal conditions which might change relation of 
G. Ht. to disch., e. g., change of control; ice or debris on control; backwater from; condition 
of station equipment £.9.C?.t:?r.<?. /....&. /<£&.{?. 

Sheet No. 1 ol....v. sheets. If insufficient space, use back of sheet, with reference letters. 

July. 1914 



388 



ELEMENTS OF HYDROLOGY 



TYPICAL DISCHARGE MEASUREMENT NOTES 

Date July Zf i9H0 ,. No. of Mea» _ 

<?//g/-/<?// K\**t,^...&.e.!rm*tfL..£A^.C€k. 





Depth 


Depth 
of ob- 
servat. 


Rev- 
olu- 
tions 


Time 
in sec- 
onds 


VELOCITY 


Area 


Mean 
Depth 


Width 




from 
initial 
poia.t 


At 

point 


Mean 
in ver- 
tical 


Mean 
in sec- 
tion 


Discharge 


zs 


33 


.8 


70 


AO 


3.93 


3.68 
















3.1 


60 


40 


3.40 




3.68 


7-8 


33 


Z 


Z8.7 


30 


33 


.3 


70 


33$ 


4.oa 


3.68 
















,?./ 


06 


40jr 


3.36 




366 


77 


383 


z 


Z8.3- 


3Z 


3.& 


.3 


70 


40 


3.33 


3.68 
















3.0 


60 


40 


3.4a 




3 73 


76 


3.8 


z 


Z8.3 


34 


3.B 


.8 


70 


40 


3.93 


3. 73 
















3.0 


70 


44 


3.60 




3.73 


3.1 


443 


z 


30.Z 


36 


4.3 


.9 


70 


40 


3.33 


3.63 
















3.4 


60 


44 


3.40 




3Z6 


8.8 


44 


z 


ZB.T' 


33 


43 


.3 


70 


4Zi 


37Z 


Z.8S 
















36 


4o 


46 


/.98 




Z.64 


30 


^.3 


z 


Z38 


40 


43 


3 


70 


43% 


3.64 


Z44- 
















3.6 


30 


S6 


/■Z3 




Z.66 


e.o 


4.3 


Z 


Z4J 


4Z 


4.3 


.9 


70 


44 


3.60 


Z93 
















3.6 


40 


40 


Z-Z6 




Z.94 


3.6 


43 


z 


Z33 


44 


4/ 


.8 


60 


33 


3.48 


Z94 
















3.3 


~30 


47 


Z.4/ 




3.04 


3.0 


4.0 


z 


Z43 


46 


39 


8 


60 


40 


3.4C 


3/3 
















3.1 


SO 


33 


£30 




3/8 


7.4 


37 


z 


Z3.3 


46 


3.S 


.7 


70 


4S 


33Z 


3.ZZ 
















Z.8 


60 


4ei 


Z.9Z 




3./S 


6.6 


33 


z 


Z0.8 


3C 


3J 


.6 


70 


'43-k 


364 


3.O0 
















z.s 


*30 


43 


Z.3I 




3.24 


6J 


3.0s 


z 


/3.8 


























Trials 
















34.7 






303:0 



No. 3 of & Sheets. Comp. by ^. &^r. 



Chk. by _£ &.^. 



STREAM-FLOW DATA 



389 



■"-«-§ 













































a 

z 








o 














O 
LU 

mo 




\ 




3 ^>v 


cv 


^ ^ 










a. 

1- 

UJ 
LU 










«4 




°7a 3 


©^s. 






z 

? > 

b 














* 


'** 


^^ 




tj 


o 
u 








S*<^ 


c^ 












LU 

UJ => 










=^o" 


t'.bh "" 


(M o 


CO 






Ul 

< 

3 g 






•-C 


o 




•*tlQ- 


^ 


-" ^ — 


„ — 




CO s 

z 






£ 


a-\- 














— 


< 










iQ 




















% 


\ N 

1 \o 






















* \ 

v\ 
















CO ss 
o . 

■W " O H Jl « . 

r-i »m .»)< *M "^ *1 S* OB 

... G 

£i (5 ^ e3 

CC t» 115 !D t^ CO O P 

ooooooo . 

T50C505C5CJ5C75 t>> 

.S ; s = : = : o 

d a 
a 8 

CD 

s 




\r 
















^ \ 


k CO 
















\<N 
















*"" 


's\ = 












































ca 


^ci 



so c5 



9 - 









so »fi 



390 



ELEMENTS OF HYDROLOGY 



be plotted in addition to the discharge curve. The mean ve- 
locity is determined by dividing the measured discharge by 
the cross-sectional area of the stream at the gaging station, and 
not at the meter section, in case the two are not identical. 



TYPICAL DISCHARGE TABLE 

Ottertail River (at German Church) near Fergus Falls, Minn. 
October 29, 1913 to September 30, 1916 



60 
O 


at 
t- . 

c3 m 

% 6 

5 


a ■ 
Q 


J3 

5? 

bO 

o 


6 

so 

a orj 

% 6 

5 


£ 

a . 

Q 


a" - 

bt 

a 

o 


M 

oS <n 
XI ^ 

5 


a 

e . 

to » 




.SP 
5 ® 

b« 




0J 
M 

5 


d . 
oj in 

to ° 

5 


1.00 


140 


18 






24 






42 






62 


1.10 


158 


19 


1.60 


261 


27 


2.10 


434 


46 


2.60 


704 


65 


1.20 


177 


19 


1.70 


288 


31 


2.20 


480 


50 


2.70 


769 


68 


1.30 


190 


20 


1.80 


319 


35 


2.30 


530 


54 


2.80 


837 


71 


1.40 


216 


21 


1.90 


354 


38 


2.40 


584 


58 


2.90 


908 


74 


1.50 


237 


24 


2.00 


392 


42 


2.50 


642 


62 


3.00 


982 





The above table is not applicable to ice or obstructed channel conditions. It is based on nine 
discharge measurements made during 1913, 1914, 1915, and 1916 and is well defined between 237 
c.f.s. and 837 c.f.s. 

The curve of mean velocity will indicate the effect of changes 
in stage if the gage is located a considerable distance above 
the control. The nearer the gage is to the control, the less 
the effect of change in stage. On a rising stage the slope of 
a stream between successive points of control is greater, and 
hence the velocity greater, at the same stage, than on a falling 
stage. 

If, through floods, the control at the gage is changed, a 
new discharge curve must be prepared. If the channel is so 
unstable as to be continually shifting, frequent discharge meas- 
urements are imperative, and the determination of the daily 
discharge becomes a relatively difficult matter.* 

* This phase of the subject is fully discussed by Hoyt & Grover in their 
"River Discharge'' and in Water Supply Paper, No. 371, p. 117; and No. 345, 
p. 53. 



STREAM-FLOW DATA 



391 



Effect of Ice on Discharge. — The friction due to ice cover 
is very much greater than that due to air; consequently, a given 
amount of water, flowing in an open channel, can only be carried 
in an ice-covered channel on an increased slope or through an 
increased area of cross section. The result is a higher stage, 
under ice cover, for the same discharge. 
11 



10 





















O1906 


















1906 O 


1906 


O 1905 














1907 


O1907 


O 
1910 


Q 1906 


ffl 1905 












1908 

O 


1910 




O 1909 
1910© 
61909 
1906 ffi 


1906 
6 « 
1906 


^90> 








c 


O1909 
1909 


O 
1908 


1907 6 


61907 














1912 




1908© © 
19086 


™*/v 


\f 










19110 C 


1911 oi91 

o 

f,1911 


3 « * 

61912 


e 1909 

190! Vo^ 
















1913 C 
1912 
1912 


O1910 
1913 e 










LEGEND 
O Gage height to water surface 
© Gage height to bottom of ice 




1 

1912 w 19 


lie m? 

il911/ 




















^912 























200 



400 



600 



800 1,000 1,200 1,400 1,600 1,800 2,000 2,200 
Discharge in Second - Feet 
From U.S.G.S. Water Supply Paper No. 337. 

Fig. 257. — Relation between Open- Water Curve and Ice Measurements, 
Red River at Grand Forks, Minn. 

The increased frictional resistance due to ice cover is well 
shown by the shape of the vertical velocity curve in Fig. 250 
and the location of the winter discharge measurements with 
respect to the discharge curve of Fig. 257. 

When the control remains open all winter, and free from 
anchor ice, the daily discharge may be determined from the 



392 



ELEMENTS OF HYDROLOGY 



observed gage heights and the open-water discharge curve. 
When ice forms over the control, however, no constant relation- 
ship exists between gage heights and discharge. 

The best results appear to be obtained from frequent meter 
measurements combined with a study of the temperature and 
its effect on the regimen of the stream.* 

Under ice conditions, velocity measurements are made at 
.2 and .8 depth, measured from the bottom of the ice. Gage 
heights are determined by chopping the ice away around the 
gage and reading the height of the water itself. Usually weekly 
readings are sufficient during the frozen season. 



Distances in feet 
.40 50 




CURVES OF EQUAL VELOCITY 



From U.S.G.S. Water Supply Paper No. 337. 

Fig. 258. — Curves of Equal Velocity in Ice-Covered Channel Cannon 
River at Welch, Minnesota. 

Fig. 258 shows curves of equal velocity of water in an ice- 
covered channel, and Fig. 259 shows the average duration of 
the ice period on the principal rivers of the United States. 

Other Methods of Measuring Stream Flow 

Float Measurements. — Floats were generally used in hydro- 
metric work until 1880. Since then, they have been gradually 
displaced by current meters. At present, floats are seldom 
used except under unusual conditions, such as at time of flood 
or in connection with reconnaissance work. 

* See U. S. G. S. Water Supply Paper, No. 337, "The Effects of Ice on the 
Flow of Streams" by W. G. Hoyt, 1911; also No. 187 by Barrows & Horton. 



STREAM-FLOW DATA 



393 



_ 

Average ice period from winter of 187G-77, to winter of 1895-96 inclusive 


Location Nov. Dec. Jan. Feb. Mar. 1 April May 


MISSOURI RIVER 


Fort Benton, Mont. 
Buford, N.l>. - 
Bismarok, N.D. 
Pierre, 8.D. 
Yankton, 8.D. 
Sioux Chy, Iowa 
Omaha, Neb. 
Nebraska City, Neb. 
SuJoeeph, Mo. 
Leavenworth, Kan. 
Kansas City, Mo. 
Jefferson City. Mo, 
SLCharles, Mo. 




























































" 


# 


YELLOWSTONE RIVER 














RED RIVER OF THE NORTH 


Moorhwd, Minn* 
St Vincent, Minn. 

Winnipeg, Man. 


| i 


































MINNESOTA RIVER 














MISSISSIPPI RIVER 


Bralnerd, Minn. 
St. Paul, Minn. 
Lake Pepin 
La CrosBe, Wis. 
Dubuque, Iowa 
Davenport, Iowa 
Rock Island, HI. 
Pea Moines Rapldf 
Keokuk, Iowa 
Quincy, TIL 
St-LouiB, Mo. 
Cairo, 111. 




















































"I 
























■- 




ST. CROIX RIVER 














ILLINOIS RIVER 


Morris, 111. 
Seneca, 111. 
Hennepin, 111. 
Peoria, 111. 
Moredoeia, 111. 
PearL 111. 






1 
























OHIO RIVER 


Pittsburgh, Pa. 
Cincinnati, Ohio 
Cairo, HI. 






H 








KANAWHA RIVER 


Charleston, W.Va. 
Point Pleasant, W.Va. 






mm 










SUSQUEHANNA RIVER 


IMbolstown, Pa. 
Harrlsburg, Pa. 








I 


CONNECTICUT RIVER 


Tuners Falls, Mass. 
Hartford, Conn. 
























MERRIMAC RIVER 




GENESEE RIVER 

















From Report of U. S. Deep Waterways Commission. 

Fig. 259. — Average Duration of Ice Period. 



394 ELEMENTS OF HYDROLOGY 

Floats may be classed as surface, subsurface, and rod floats. 
Surface floats consist of light objects, such as wood or corked 
bottles, whose velocity when floating on the surface of the 
water is measured directly by observing the time required to 
pass a given distance. The mean velocity in the vertical will 
be about 85 per cent of the surface velocity. 

Subsurface floats consist of a relatively large submerged 
object attached, by means of a line, to a light marker floating 
on the surface. The subsurface float can be arranged to float 
at any depth, and hence will give an approximate value for mean 
velocity directly. This type of float was used by Humphreys 
and Abbot in gaging the Mississippi River in 1851 and 1858.* 

In general, subsurface floats give better results than surface 
floats but are less accurate than rod floats. 

Tube or rod floats consist of a tin tube or a wooden rod from 
one to three inches in diameter, of such a length and so weighted 
as to float at a depth as nearly equal to the full depth of the 
channel as possible. Rod floats are best adapted to regular 
or artificial channels. The mean velocity is computed by 
the Francis formula: 

Vm = Vr { 1.000 - 0.116 (VD - 0.1) j, 
in which 

Vm — mean velocity in vertical; 
Vr = observed rod float velocity; 
D = proportion of depth not reached by rod. 

Considerable precision has been secured in making rod float 
measurements of the Mississippi River at St. Louis since 1900. f 
In April, 1912, gagings were made at observed rod velocities 
ranging from 7 to 12 feet per second, and a gage height of 30.7 
feet. Floats up to 46 feet long were used. The width of the 
stream at the gaging station was about half a mile. 

* Report upon the Physics and Hydraulics of the Mississippi River by 
Humphreys and Abbot, 1861, p. 224. 

t Mississippi River Gagings by Rod Floats by Frederick Y. Parker; Pro- 
fessional Memoirs, U. S. Corps of Engineers, Vol. V, p. 724. 



STREAM-FLOW DATA 395 

In making float measurements a range about 200 feet in 
length is selected on a portion of the channel that is as straight 
and uniform in depth and cross section as possible. The ve- 
locity is measured at from five to twenty or more float stations, 
spaced as nearly equidistant across the channel as possible. 
Every float course is carefully sounded, and from the mean 
velocities and areas of the subdivisions of the cross section of 
the stream, partial discharges are computed and from these 
the total discharge of the stream is secured. The detailed 
method to be adopted in any particular case will be dependent, 
mainly, upon the characteristics of the channel whose discharge 
is to be determined. One of the principal objections to float 
measurements is the amount of labor and floating equipment 
required on the work. Under favorable conditions, however, 
and when the work is carefully done, a high degree of accuracy 
can be secured. 

Slope Measurements. — The Velocity of flowing water de- 
pends upon the slope and character of its channel. As the 
friction on the bed of the stream and against its banks becomes 
relatively less effective, with increasing depth, the velocity is 
also indirectly dependent upon the mean depth. Chezy in 
1775 expressed these relations in the following formula: 



v = cvrs, 
in which 

v = mean velocity in feet per second; 

c = a coefficient depending mainly upon the character of 
the channel and varying from about 25 to 200; 

r = the hydraulic radius, or area of cross section in square 
feet divided by the wetted perimeter in feet. (In 
natural channels this is approximately equal to the 
area divided by the width plus the mean depth.) 

s = the slope, or feet fall per foot. (To be determined 
by leveling.) 



396 ELEMENTS OF HYDROLOGY 

The coefficient c may be calculated by Kutter's formula: 

s n 

c = 



{ .00281 ) n 

It has been found by repeated measurement that, for the 
same channel conditions, the coefficient n in the Kutter 
formula decreases with increase in depth. This appears to 
be due, in part at least, to the lesser effect, at high stages, 
of eddies due to irregularities in the channel bed. 

Simple diagrams for the solution of Kutter's formula are 
those given by Kennison in Engineering News, June 20, 1912, 
p. 1191; and by Fish in Engineering News, April 15, 1915, 
p. 733. 

Another formula frequently used in the determination of 
the coefficient c is the Bazin formula: 

87 
c = 

.552 + -^ 

Vr 

Hillberg f found that a simple relation exists between the 
coefficients used by Bazin and by Kutter. He expressed this 
relation by the equation : m = 87 n — 1 . 

The best values of n for use in Kutter's formula are those 
given by Horton % in the following table. The equivalent 
values of m in Bazin's formula have been computed by means 
of Hillberg's formula and added for use in determining c. 

Whenever the slope of a channel is greater than 1.5 feet per 
mile, the slope term in Kutter's formula has relatively little 
effect on the value of c. This fact is shown in Fig. 260. The 
relation between r and c is shown in Fig. 261. When r = 3.28 
feet the value of c is independent of the slope and its value 

1 811 

is — '- The effect of variations in n on the value of c is 

n 

shown in Fig. 262. 

* Ganguillet & Kutter, The Flow of Water in Rivers and other Channels. 
t Hillberg, A. G., Engineering Record, Oct. 21, 1916, p. 494. 
% Horton, Robert E., Engineering News, Feb. 24, 1916, p. 373. 



STREAM-FLOW DATA 



397 







to 




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398 



ELEMENTS OF HYDROLOGY 



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s and ditches: 
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al stream channels 
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ien dooIs 


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STREAM-FLOW DATA 



399 



so 

>T5 



























































n — 0;03- 










V 






















\ 


-— 






/•=io 




» = 0.03 








































r=5 




«=0.03 


















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n = 0.03 






























































r=1.0 




» = 0.03 
































.0002 .OOftt .0006 .0008 .0010 .0012 .0014 .0016 .0018 .0020 
Slope "s" 



0.6 1.0 1.5 2.0 2.5 3.0 



.i.0 5.0 6.0 

Slope- Feet per .Mile 



Fig. 260. — Effect of Slope of Channel on Value of Coefficient c. 



































«-°e- 


















,„.ooot 


a^B— 


















ysiu^ — 
































































































EFFECT OF HYDRAULIC RADIUS 

ON 

VALUE OF COEFFICIENT "c" 















































































10 15 

Hydraulic Radius ' V" in Feet 

Fig. 261. 



220 
200 

180 
- 160 
•^ 140 
I 120 

1 100 



40 



20 











| 
















EFFECT OF ROUGHNESS 

FACTOR "n" ON 

VALUE OF COEFFICIENT "c" 


































>S^ 


$ 










^^ 










S = .00W 























.01 .02 .03 .04 .05 .06 

Rougnaess Factor "«-" in Kutter's Formula 

Fig. 262. 



400 



ELEMENTS OF HYDROLOGY 



Changes in temperature have a very appreciable effect on 
the flow of water. Butcher * has reduced the experimental 
results of Mair and Saph and Schoder to the uniform basis 
of a velocity of 6 feet per second with the following results: 



Experiments by Mair 


Experiments by Saph and Schoder 


Temp. deg. F. 


Values of c. 


Temp. deg. F. 


Values of c. 


57 
70 
80 
90 


117 
120 
121 
123 
125 
127 
129 
130 
136 


40 
55 . 
70 


10S 
112 
116 


100 






110 






120 






130 






160 













The determination of the flow of streams from measurements 
of the slope of the water surface and the cross-sectional area 
finds its principal application in connection with flood discharges, 
backwater due to dams and similar obstructions, and the dis- 
charge capacity of artificial or improved natural channels. 

In backwater computations the coefficient c or n can be 
determined directly by measurement in the upper and critical 
reaches of the stream. In computing the increased discharge 
capacity of channels under improvement similar determinations 
of c will be of great assistance. Where the channel depths 
vary greatly as in cases of overflow, the cross section should 
be subdivided and different values of c used for the different 
portions of the section. 

The Chemical Method. — The principle involved in the 
measurement of the flow of water through turbines, in canals, 
or in natural channels, by the use of chemicals, is very simple. 
If S pounds of chemical are added, each second, to a stream 
discharging Q cubic feet of water per second, and if, after 
the chemical has become uniformly distributed through the 

* Butcher, W. E., Engineering News, 1916, Vol. LXXVI, p. 326. 



STREAM-FLOW DATA 401 

water, a sample of the dosed water tests 1 pound of chemical 
in W pounds of water, then: 

S l_ m ws 

62.5 Q W ° r Q 62.5' 

The chemicals most commonly used are sodium chloride 
(common salt) and calcium chloride. Sulphuric acid, caustic 
soda and bicarbonate of soda have also been used. The best 
chemical for each particular instance usually depends, mainly, 
upon the chemical constituents of the water to be tested. When 
the ratio of dilution is to be determined by the color of the water, 
an aniline dye is used. 

Although the principle involved in chemical measurements 
of the flow of water is simple, yet extensive refinements are 
necessary in its practicable application, if a high degree of 
accuracy is to be attained. The principal difficulties involved 
in this method lie in securing uniform composition in the dosing 
solution and a thorough mixture of the solution with the water 
before the sample from which the ratio of dilution is to be 
determined is taken. 

In order to secure an accuracy of less than one per cent, 
it is necessary to use a quantity of salt solution which will give 
a ratio of weight of salt to weight of dosed water of at least 
one part in 75,000 to 25,000 according to the method used in 
testing for the salt. 

Perhaps the best method of determining the ratio of dilution 
when the water is dosed with sodium chloride is by titrating 
for the chlorine by the use of silver nitrate and potassium chro- 
mate. The addition of silver nitrate to the salt solution pre- 
cipitates the white silver chloride. By keeping the proper 
amount of potassium chromate indicator in the solution, the first 
drop of silver nitrate in excess of that required to precipitate 
all of the sodium chloride will change the color of the solu- 
tion to orange. Knowing the degree of concentration of the 
silver nitrate solution and the amount used in precipitating 
all of the sodium chloride in the given quantity of water, the 



402 ELEMENTS OF HYDROLOGY 

ratio of dilution becomes known. As a matter of convenience, 
the concentration of the silver nitrate solution may be so ad- 
justed that the volume of this solution consumed in precipitating 
the sodium chloride is numerically equal to the weight of the 
salt in the volume of water tested. One gram of silver nitrate 
will precipitate .344 gram of salt. 

A dosing solution of 300 grams of sodium chloride per liter 
of water is a satisfactory strength to use. When large quan- 
tities of water are to be measured, the ratio of dilution adopted 
for the purpose of limiting the amount of dosing solution re- 
quired may be so great as to necessitate the evaporation of 
some of the water from the sample so as to give a degree of 
concentration which will admit of sufficiently accurate deter- 
minations of the amount of dosing chemical present in the 
sample taken for test. A half liter of dosed water is a satis- 
factory size of sample to use. This may be evaporated to 
about 10 c.c. for titration. 

The accuracy of titration is dependent upon the amount of 
silver nitrate used in precipitating the chlorine. As the burette 
used for dropping the silver nitrate into the sample can readily 
be read to about .1 c.c, a titration which requires 40 c.c. of 
silver nitrate will give an accuracy of well within one quarter 
of one per cent. 

It has been shown by Mellet * and Groat, f in actual tests, 
that silver nitrate titrations for chlorine can be made with an 
accuracy of one tenth of one per cent. 

One and one half grams of silver nitrate per liter of distilled 
water for the silver solution and 50 grams of potassium chro- 
mate per liter for the indicator are satisfactory concentrations 
to use for these solutions. 

The silver nitrate solution may be made up at ten times 

* Mellet, R., Bui. Technique de la Suisse, Romande, Nr. 11, 10 Juin, 1910, 
Lausanne. 

t Groat, Benj. F., Chemi-Hydrometry and its Application to the Precise 
Testing of Hydro-electric Generators, Proc. Am. Soc. C. E., Vol. XLI, Nov., 
1915, p. 2103. 



STREAM-FLOW DATA 403 

the required strength and kept away from the light. A small 
amount is then taken and properly diluted for use in titrations. 
About one drop of potassium chromate indicator is required 
for each 10 c.c. of silver nitrate used in precipitating the chlorine. 
Groat found that 30 to 40 inversions of the bottle are required 
to secure a good mixture of chemicals when making titrations. 

In measuring the flow of water, titrations for chlorine should 
be made of samples of the normal untreated water in the stream, 
of the dosing solution used, and of the salted water after the 
dosing solution has become thoroughly mixed with the water. 
The methods to be applied in dosing and sampling the water 
are dependent, primarily, upon the character of the stream to 
be measured, whether a mountain torrent, a brook, a large 
sluggish stream, a canal, or a tailrace. 

In canals and headraces, the dosing solution may be forced 
into the water through |- to j-inch openings in several lines 
of horizontal pipes, under considerable pressure, maintained by 
a 6- or 8-inch centrifugal pump into whose suction pipe the 
dosing solution is pumped by a smaller centrifugal pump. 
Samples of the dosed water are drawn up through perforated 
pipes each having its individual pump. 

Groat found in testing power plants, that 5 or 6 minutes were 
required after starting to dose the water in the headrace, before 
conditions of flow in the tailrace had become steady. He 
also found that about 15 minutes were required for a satisfactory 
run. 

A discussion of all the refinements required to secure accurate 
results is beyond the scope of this treatise. A full discussion 
of the chemical method of measuring the flow of water will 
be found in the papers of B. F. Groat, in Proc. Am. Soc. C. E., 
November, 1915, pages 2103 to 2427, and Proc. Eng'r Soc. of 
Western Penn., May, 1914, Vol. 30, page 374, from which the 
above comments have been largely drawn. 

Diaphragm or Traveling Screen.— Where an extremely uniform 
cross section of channel is available, such as a concrete or timber- 



404 ELEMENTS OF HYDROLOGY 

lined canal, very accurate measurements of mean velocity can 
be made by observing the rate of travel of a vertical diaphragm 
or "screen" made of light material and accurately fitted to the 
cross section of the channel. By recording the velocity over 
a measured base 50 to 100 feet in length, by means of electrical 
contacts at each end, a record of the mean velocity of the flow- 
ing water is secured directly. The only correction required 
is for leakage around the edges of the screen. This depends 
principally upon the closeness of the fit and the force required 
to move the screen. Usually this correction is small as the 
necessary clearance at the edges of the screen may be reduced 
to about one half inch or less, and the velocity of the water 
at the extreme sides of the channel is less than the mean. 

The method of measuring the flow of water by means of 
diaphragms or traveling "screens" was invented by Prof. 
Erick Andersson of the University of Stockholm about twelve 
years ago.* This method has been used to a considerable ex- 
tent in Europe, particularly, by the large manufacturer of hy- 
draulic turbines, J. M. Voith, of Heidenheim, Germany, but 
it is almost unknown in the United States. The Voith appara- 
tus is shown in Fig. 263. 

Among the advantages of the diaphragm method are its 
great accuracy and sensitiveness to velocities as low as a few 
hundredths of a foot per second, and the fact that the results 
are known immediately so that measurements can be repeated 
at once in case they fail to check. 

The Pitot Tube. — The Pitot tube has long been used for 
measuring the velocity of water, but not until recently have 
its possibilities been fully appreciated. Any pipe with its stem 
vertical and its lower end bent into the direction of the current, 
so that the opening faces upstream, constitutes a simple form 
• of Pitot tube. Many forms of tubes have been in use, but the 

* The Diaphragm Method for the Measurement of Water in Open Chan- 
nels of Uniform Cross Section, by C. R. Weidner, Bui. No. 672, University of 
Wisconsin, 1914. 



STREAM-FLOW DATA 



405 



shape of the orifice is no longer considered important. This 
was clearly demonstrated by White * in 1900. 




Courtesy University of Wisconsin. 

Fig. 263. — Measuring Discharge with Traveling Diaphragm. 

The Pitot tube indicates a head equal to the velocity-head 
of the water impinging on its orifice, plus any static head under 
which the given filament of water is flowing. It has been found 
that if h is the velocity-head indicated by the tube, the 
velocity of the water is substantially equal to 98 per cent of 
V2 gh. It should be added, however, that the formula v = c \gh 
instead of v = c V 2 gh still has its adherents. 

In making determinations of flow with the Pitot tube it is 
usually far more difficult to measure the pressure-head than the 
velocity-head. The old forms of Pitot tubes in which the 
pressure-head was determined by means of an orifice placed 

* White, W. M., Jour. Assoc. Engr.'Soc, 1901, Vol. XXVII, p. 35. See 
also Moody, L. F., Proc. Engr. Soc. of Western Penn., 1914, Vol. XXX, p. 
279; and Groat, B. F., ibid., p. 324. 



406 



ELEMENTS OF HYDROLOGY 



parallel to the direction of the current and alongside of the 
dynamic orifice were particularly subject to error. 

When the flow of water is turbulent, the Pitot tube records 
the mean velocity-head which corresponds to the mean of the 
squares of the instantaneous velocities. 

For best results the Pitot tube should not be rated by 
drawing it through still water but by comparing the known dis- 
charge of a pipe line, a Venturi meter throat, or a jet, with the 
discharge determined by means of the Pitot tube on the basis 
of the area of the cross section of the 
stream of water measured and the dis- 
tribution of velocities in the cross 
section as ascertained by means of 
"traverses" with the tube. 

The Pitot tube finds its most common 
application in the measurement of the 
flow of water in pipes. A form of tube 
with a recording device, known as the 
Cole Pitometer, illustrated in Fig. 264, 
is most commonly used for this pur- 
pose. 

The Venturi Meter. — Perhaps the simplest device for 
measuring the flow of water is the Venturi meter, invented 
by Herschel in 1886. The essentials of the Venturi meter 
are shown in Fig. 265. The area of contracted section or 
" throat " is from \ to I of the area of the pipe line. At the 
throat of the meter the velocity is increased in proportion to 
the decrease in area and part of the pressure-head is transformed 
into velocity-head. The difference between the indicated 
pressure-head in the pipe and that at the throat of the meter 
represents the velocity-head corresponding to the known in- 
crease in velocity caused by the reduction in cross-sectional 
area, plus a small amount of head lost in friction. The discharge 
of the meter is given by the equation : 




Fig. 264. — Cole Pitometer. 



STREAM-FLOW DATA 



407 



Q = CA t 



2gh 



1 - 



Ar, 



where h is the difference in pressure-heads at the section of the 
meter where the area is A p and that at the throat where the 
area is A.. The coefficient c varies from .97 to .99. 




Fig. 265. —The Venturi Meter. 



The greater the contraction at the throat of the meter the 
greater the difference in pressure-heads and, hence, the greater 
the accuracy of the readings but also the greater the friction 
loss. This loss, however, is very small, although it is continuous. 
It is independent of the pressure in the pipe line or penstock; 
consequently the power loss becomes relatively smaller with 
increased head. It varies from about one tenth to one half 
of one per cent. The loss in the meter can be reduced to a 
minimum by tapering the diverging portion very gradually, 
because eddy losses are much more likely to occur in the di- 
verging portion of the stream than in the converging portion. 
This fact is well illustrated in nature by the shape of a fish. 
The improved construction of modern large-size meters, result- 
ing in small losses, has led to an increasing use of this device 
for measuring the flow of large quantities of water. 

Large Venturi meters are commonly built up in three parts. 
The approaches are often built of concrete, wood stave, or riv- 
eted-steel pipe, the throat, only, being a carefully machined 



408 ELEMENTS OF HYDROLOGY 

casting, usually of bronze. Meters as large as 18 feet in diam- 
eter are in successful operation. Venturi meters themselves 
require neither attention nor repairs. The only maintenance 
required is for the small upkeep of the recording devices where 
a continuous record of flow is secured. 

Hazen * has called attention to the fact, that, since Venturi 
meters indicate velocity-head, or the square of the instantaneous 
velocity, they will over-register from 3 per cent to 5 per cent 
on lines when great and rapid fluctuations occur in the flow. 

This, of course, is due entirely to the recording device. Under 
ordinary conditions of turbulence, the over-registration is neg- 
ligible. 

STREAM-FLOW DATA FROM WATER-POWER PLANTS 

It is often possible to extend the available records of stream 
flow by utilizing records of water levels above and below dams. 
The flow over dams can be computed by means of the formula: 

Q = clHi, 

in which c is a coefficient varying from about 3.0 for unfavorable 
spillway profiles and small values of H to about 3.8 for the 
best curved profiles and large values of H; I is the length of 
spillway crest in feet; and H the head on the crest, measured in 
quiet water back of the dam. When flashboards are in use a 
value of 3.33 should be used for c. 

In case of end contractions the length of the spillway should 
be reduced by .1 H for each end although in long spillways 
this correction is negligible. When the cross-sectional area of 
the stream is about 5 times the area of the over-falling sheet 
of water the effect of velocity of approach is negligible. 

The flow through submerged sluice gates is usually proportional 
to the square root of the head on the center of the opening. 
The coefficient of discharge will vary greatly with the shape 
of opening and the approach, but will lie between .60 and .95, 
usually approaching the lower value. 

* Hazen, Allen, Engineering News, August 17, 1916, p. 293. 



STREAM-FLOW DATA 409 

The flow through power houses can be determined from records 
of power output or gate opening, and head- and tail-water levels 
by rating the installation by actual meter measurements or 
by using the manufacturer's rating of the turbines, or Holyoke 
tests if these are available. When a turbine installation has 
once been well rated for various heads and gate openings, good 
records of stream flow can be secured if a continuous record 
of operation is kept at the plant. 

WHERE STREAM-FLOW DATA ARE PUBLISHED 

The principal sources of stream-flow data in the United States 
are the publications of the Water Resources Branch of the 
Geological Survey. This Branch was maintaining 1741 stations 
in 1914, and while in most cases the records extend back only 
a comparatively few years much extremely valuable information 
has been collected by uniform methods. 

Other important sources of information are the U. S. Census 
Bureau, the U. S. Weather Bureau, the U. S. Army Engineers, 
the reports of State and City officials and Special Commissions. 

Data for Canada are being published by the Dominion Water 
Power Branch, Ottawa, Canada. 

These various sources of information should always be con- 
sulted by the engineer before undertaking to make his own 
measurements. 



CHAPTER XI 

SUPPLEMENTING STREAM-FLOW DATA 

Unreliability of Short-Term Means. — On comparatively few 
streams of the country do the records of discharge extend over 
a long term of years. Short-term records do not give the 
extremes of high and low flow unlessHay sheer accident such 
years have been included in the term over which observations 
extend. Short-term records, moreover, do not give a satis- 
factory value for mean utilizable flow. In the last analysis, 
it is usually necessary to supplement the observed stream-flow 
data with computed values based on rainfall and other physical 
data, in order to arrive at a probable maximum, minimum, and 
mean utilizable flow for any given stream. 



dl20 































CUMULATIVE MEAN 

RAINFALL AND RUN-OFF 

MISSISSIPPI RIVER 




















































































































































































S-' 
















r-"" 




"--- 


^ Run-off 










\ 












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/ 








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Ilain 


"all 






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36.0 § 



s w 



5.0 



3 i 5 G 7 8 9 10 11 12 13 11 15 16 17 
Period of Years 
Fig. 266. 



The curves of Figs. 266 to 268 show the annual and periodic 
variations in rainfall and runoff on the Tohickon Creek and the 
Mississippi River watersheds. 



410 



SUPPLEMENTING STREAM-FLOW DATA 



411 



The curves of cumulative mean rainfall and runoff represent, 
at every point, the mean of all the annual values preceding. It 
is interesting to note that on the Mississippi River watershed 



no 



,2130 



120 



110 



100 



!)0 















1 




















































































/ 




x 














































; 








































































































\ 














CUMULATIVE MEAN 

RAINFALL AND RUN-OFF 

TOHICKON CREEK 
















/ 








































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65 



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P30 



55 fl 



50 



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2.1 



15 



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 
Period of Years 

Fig. 267. 



140 






1 1 1 1 1 1 1 1 1 1 








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PROGRESSIVE FIVE-YHAR MEAN 
RAINFALL AND RUN-OFF 














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120 


















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SO 












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1890 91 92 93 94 1895 96 97 98 



99 1900 01 02 03 041905 06 07 08 09 191011 12 13 14 1915 

Fig. 268. 



the 12-year mean runoff differs from the 6-year mean by more 
than 20 per cent. The 12-year mean rainfall, however, differs 
from the 6-year mean by only a small percentage. On the 
Tohickon Creek watershed the 5-year mean rainfall is 111 per 
cenu of the 24-year mean, and the 5-}^ear mean runoff is 123 



412 ELEMENTS OF HYDROLOGY 

per cent of the long-term mean. Though the variation in run- 
off is proportionately very much larger than the variation in 
rainfall, the actual variation in inches of rainfall and runoff is 
practically the same for the Tohickon Creek watershed, but the 
variation in inches of rainfall is very much greater than the 
variation in inches of runoff on the Mississippi River watershed. 
This difference exists on all watersheds having similar differ- 
ences in annual rainfall and in evaporation and transpiration 
losses. On the Tohickon Creek watershed, the normal annual 
rainfall is sufficient to supply the needs of evaporation and 
transpiration; consequently, speaking in very approximate 
terms, most of the rainfall in addition to those needs appears 
as runoff, as has been pointed out frequently in the past. On 
the Mississippi River watershed, however, and throughout the 
greater part of the United States, the normal rainfall is insuf- 
ficient to supply the needs of transpiration and evaporation at 
the prevailing temperatures; consequently, a large portion of 
any increased rainfall goes to supply unsatisfied needs of tran- 
spiration and evaporation, and hence a comparatively small 
portion of the increased rainfall, within certain limits, appears 
as runoff. 

Sargent * comments briefly on long-term variations in stream 
flow on the Croton and Hudson rivers. It appears from these 
records, in so far as low water is concerned, that the rate of 
flow for the 5 driest months at Mechanicsville, on the Hudson 
River, was lowest in 1908 and highest in 1905. It was about 
one third as much during the former year as during the latter. 
It also appears that the rate of flow which occurred 70 per cent 
of the time during the 5 years, 1909 to 1913, was only a little 
more than one half of that which occurred 70 per cent of the 
time during the 26 years from 1888 to 1913, even though the 
extreme minimum rate of flow was practically the same in the 
two periods. 

Fig. 268 shows the progressive 5-year mean rainfall and run- 
* Engineering News, December 3d, 1914. 



SUPPLEMENTING STREAM-FLOW DATA 413 

off for the Mississippi River and Tohickon Creek watersheds. 
These curves bring out forcibly the great differences which 
exist, particularly in runoff, between the average values derived 
from short-term — that is, in this case, 5-year — records. 

If the conclusion as to mean annual runoff for the Mississippi 
River watershed were based on the 5-year mean ending in 1902, 
during which period the rainfall averaged 98 per cent of the 
mean for the 17-year period, this conclusion would be 20 per 
cent too low. If the conclusion were based on the 5-year mean 
ending in 1909, during which period the rainfall was 104 per 
cent of the mean for the 17-year period, the figure would be 
40 per cent in error. If the conclusion were based on the 5- 
year period ending in 1913, during which period the rainfall was 
about 10 per cent below normal, the value adopted would be 
nearly 35 per cent too small. The maximum variation in 5- 
year means of runoff within the 17-year period over which the 
records used here extend is about 75 per cent. 

Even though on a small watershed such as that of Tohickon 
Creek, the fluctuations are not as great as they are on the Mis- 
sissippi, nevertheless, very substantial differences exist between 
the 5-year mean rainfall and runoff and the 24-year mean. 

Comparative Hydrographs. — It must be apparent from the 
hydrographs of streams presented in the foregoing pages that 
conclusions respecting the flow of one stream, based upon 
hydrographs of that of another, even though an adjacent one, are 
usually subject to gross errors. Little reliance can be placed 
upon results secured in this manner unless the characteristics 
of the two watersheds are identical. This, however, is seldom 
the case; consequently, comparative hydrographs are of little 
value for supplementing stream-flow data. 

Methods of Computing Runoff. — From time to time various 
curves and formulas designed to give the annual yield of water 
from any given watershed, and its distribution through the 
year, have been presented. Perhaps the most common expres- 
sion of these quantities has been in terms of percentage of pre- 



414 ELEMENTS OF HYDROLOGY 

cipitation. Whenever this method has been adopted, great 
variations in runoff, for the same quantities of precipitation, 
have been noted. In fact, the lack of direct relationship between 
rainfall and runoff is a fact of common observation among those 
who have made a study of such data. Runoff, for a given 
month, considerably in excess of the rainfall for the same month, 
is not an exceptional occurrence on many streams of the country. 
For the same annual rainfall the annual runoff occasionally 
varies by nearly 100 per cent on the same stream. 

These facts are well illustrated by Fig. 269.* The runoff for 
April, in Fig. 269, shows a variation of from 5 to 200 per cent 
of the rainfall on the same watershed. Moreover, the high 
percentage is for the lower rate of rainfall. The runoff for 
September shows a variation of from 2 to 140 per cent of the 
rainfall for practically the same precipitation on the same 
watershed. The annual rainfall for one of the streams on Fig. 
269 varies from 6.7 to 11.97 inches, or about 80 per cent for 
practically the same annual rainfall. 

In attempting to express the relationship between rainfall and 
runoff, Vermeulef used a constant plus a percentage for the 
several months of the year, and varied this relationship on 
different watersheds with the mean annual temperature. 

Justin t expressed annual runoff by an equation consisting of 
a coefficient (which varied with slope and mean annual tem- 
perature for different watersheds) multiplied by the square of 
the annual rainfall. 

Babb § used curves giving the monthly runoff to be expected 
from any given watershed in the various parts of the country, 
in terms of a percentage of the total annual runoff. The latter 
was computed from the annual rainfall by using a percentage 

* Compiled from "The Flow of Streams and the Factors That Modify 
It," by Prof. D. W. Mead, Univ. of Wis. 

f Water Supply of New Jersey, 1894; and Annual Report, State Geolo- 
gist of New Jersey, 1899. 

% Trans. Am. Soc. C. E., Vol. LXXVII, p. 346. 

§ Trans. Am. Soc. C. E., Vol. XXVIII, p. 323. 



SUPPLEMENTING STREAM-FLOW DATA 



415 



"71 



Monthly 



7^ 



/ 



./' 



X' 



~7^ 



April 



c 3 



?2 






/ 



s. 



5T 






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5/ 



?&£. 



^ 



u# 



.— tf D 



•trS 



RELATION OF MONTHLY 
RAINFALL AND RUN-OFF 
ON WISCONSIN STREAMS 

I I I 



4 5 6 

Rainfall, in Inches 



10 




4 5 6 

Rainfall, in Inches 



25 



20 



= 15 



910 
% 



Annual 



-/ 



A 



'/ 



/ 



/ 



s 



V + 



/ 



/ 



/ 



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W- 



y 



/ 






/ 



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Z^ 



— % 
□ 



~7^ 



» e 



.-•3 



L^ 



£' 



RELATION OF ANNUAL 

PRECIPITATION AND RUN-OFF 

ON WISCONSIN STREAMS 



20 25 30 

Rainfall, in Inches 



35 



40 



45 



50 



Fig. 269. — Lack of Relation between Rainfall and Runoff (after Mead). 



416 ELEMENTS OF HYDROLOGY 

relationship derived from a study of the mean observed relation 
between rainfall and runoff on a number of streams in various 
parts of the country. 

Rafter * used curves, which, in general, are graphs of an 
exponential equation, for the purpose of showing the relation 
between rainfall and runoff by " storage," " growing," and 
" replenishing " periods. 

Newell | expressed the general relationship between rainfall 
and runoff by two typical curves, one for streams in mountain- 
ous regions and the other for streams draining basins with broad 
valleys and gentle slopes. 

Other writers have held that 20 inches of rainfall are required 
to supply evaporation and transpiration losses, and that prac- 
tically all precipitation greater than 20 inches appears as runoff. 

Although the subject of stream flow has been ably discussed 
by the men just mentioned, the author cannot refrain from ex- 
pressing the belief that the relations between rainfall and runoff, 
indicated by the curves and formulas just referred to, are, in a 
varying degree, generalizations which bring out class likeness 
but obscure the individual characteristics of runoff from differ- 
ent watersheds, resulting from differences in the character and 
distribution of the rainfall, and the effect of temperature, veg- 
etal cover, topography, soil, and subsoil on the disposal of 
rainfall. 

In consequence, the author has worked up a " rainfall loss " 
or " hydro-physical " method of computing stream flow. The 
essentials of this method were first publicly presented in an 
address before the College of Engineering of the University of 
Minnesota about five years ago.. A more detailed presentation 
was made in a paper before the American Society of Civil Engi- 
neers, printed in the 1915 Transactions, to which the reader is 
referred. The material of this paper is being freely drawn upon 
in this discussion. 

* Water Supply and Irrigation Paper No. 80, U. S. Geol. Survey. 
., f Fourteenth Annual Report, Part 2, 1892-1893, U. S. Geol. Survey. 



SUPPLEMENTING STREAM-FLOW DATA 417 

Considering the number of streams in the United States the 
discharge of which is of industrial importance, the number of 
stations at which stream flow is being measured is compara- 
tively small, and the periods for which records are available are 
relatively short. If it takes from 30 to 40 years to secure an 
accurate measure of the mean annual rainfall at any given 
place, it is reasonably certain that the true means and extremes 
of runoff are compassed between at least as wide limits. Pre- 
cipitation and temperature are being observed in the United 
States at nearly 6000 stations. Stream measurements are being 
made by Federal and State authorities and private parties, 
together, at about one fourth as many stations. 

Notwithstanding the valuable work being performed by these 
organizations on all too meager appropriations, relatively few 
stream-flow data are available. For most streams only short- 
term records have been secured, covering by no means the 
extremes of high and low flow, or giving a dependable mean 
flow. If such measurements of stream flow as are available can 
be supplemented by reasonably accurate computed values, so as 
to give a long-term record of fair reliability, and covering more 
nearly the extremes of high and low flow, some of the uncer- 
tainty often attending efforts toward industrial utilization of the 
flow of streams and protection against floods may be eliminated. 

The " Water Year." — Frequent comment has been made on 
the fact that the calendar year is an inappropriate and conven- 
tional period into which to divide time, from a hydrological 
viewpoint. A period of 12 months, beginning December 1 and 
ending the following November 30, has been used by many 
hydraulicians and called the " water year." This " water 
year " has again been divided into three periods, viz., Decem- 
ber to May, inclusive, constituting the " storage " period; June 
to August, inclusive, constituting the " growing " period; and 
September to November, inclusive, constituting the " replen- 
ishing " period. Although this division of time is more logical 
than the calendar year, efforts to express runoff as a percentage 



418 ELEMENTS OF HYDROLOGY 

of rainfall for each of these periods are considered by the author 
hardly less futile than efforts to express runoff as a percentage 
of the monthly or annual rainfall. This is true because the 
yield of a watershed, as previously stated, is a residual of the 
precipitation and not a proportion of it. 

Fig. 270 * substantiates this view. The scale used in Rafter's 
diagrams for the growing and replenishing periods completely 
conceals the true lack of relationship between rainfall and run- 
off during these periods. At first glance one would conclude 
that the runoff during the growing and replenishing periods 
showed a much closer relationship to the rainfall than that of 
the storage period. On plotting the values for these two peri- 
ods to a scale which results in a curve comparable to that used 
for the storage period, however, quite the contrary is found to 
be the case, as shown in Fig. 271. 

During the storage period, the runoff varies from 12.8 to 22.3 
inches, or practically 75 per cent for a rainfall of between 22 
and 23 inches. During the growing period, on the same stream, 
the runoff varies from .72 to 3.07 inches, or 325 per cent for 
approximately the same rainfall. During the replenishing pe- 
riod the runoff varies from 3.76 to 1.58 inches, or 140 per cent 
for rainfalls of 13.11 inches and 12.89 inches respectively. The 
entire annual runoff from this watershed varies in 15 years 
from 12.69 inches for 39.70 inches of rainfall to 23.27 inches for 
38.71 inches of rainfall, or practically 100 per cent for the same 
rainfall. 

The author usually takes as his rainfall year, in northern 
latitudes, the 12-month period beginning November 1, and as 
the corresponding runoff year the 12-month period beginning 
the following March 1. Stream flow during the winter, in the 
northern half of Minnesota, for example, is almost entirely 
independent of the precipitation during these months, because 
such precipitation is practically all stored as snow. Stream 

* Complied from Water Supply Paper No. 80, "The Relation of Rainfall 
to Run-Off," by George W. Rafter. 



SUPPLEMENTING STREAM -FLOW DATA 



419 



















.._ , . . „.... .,..._. 1 | | 1 r 1 
































1 1 1 1 1 1 1 1 I 1 1 1 | 1 1 
































RELATION BETWEEN 

PRECIPITATION AND RUN-OFF 

IN THE SUDBURY RIVER BASIN 

DURING THE 

STORAGE PERIOD 




































































































































































































30 










































































































































































































































































































































































































































































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10 



15 20 25 

Precipitation, in Inches. 



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35 



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1 1 1 1 1 1 1 1 1 1 1 1 1 1 






























1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 






























RELATION BETWEEN 

PRECIPITATION AND RUN-OFF 

IN THE SUDBURY RIVER BASIN 

DURING THE . 

GROWING PERIOD 
































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































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Precipitation, in Inches. 



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RELATIO.N BETWEEN 

PRECIPITATION AND RUN-OFF 

IN THE SUDBURY RIVER BASIN 

1 DURING THE 

REPLENISHING PERIOD 


























































































































































































































































































































































































































































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10 15 20 

Precipitation, in Inches. 

Fig. 270. — (After Rafter.) 



25 



30 



420 



ELEMENTS OF HYDROLOGY 



PRECIPITATION AND RUN-OFF 
SUDBURY RIVER 





































/ 




































































GROWING PERIOD 












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Precipitation, ia Iucbes 

Fig. 271. 



iSS 



SUPPLEMENTING STREAM-FLOW DATA 421 

flow, in such latitudes, is dependent on the water stored in the 
ground and in lakes during the previous open seasons. 

In the greater portion of the United States, a 12-month 
period beginning August, September, or October 1, when the 
ground and surface storage are both reduced to a minimum, 
affords a satisfactory " water year." Usually, however, the 
annual yield of a watershed, even in such " water years," is 
modified somewhat by ground storage. 

The author computes the annual runoff entirely by calendar 
months, without any attempt to adhere to a division of the year 
into " storage," " growing," and " replenishing " periods, or 
into spring, summer, fall, and winter seasons. 

The Author's Evaporation Curve. — The variation of evapo- 
ration from land areas with changes in seasons, monthly mean 
temperature, and monthly mean rainfall, based on the author's 
study of the subject, is summarized in the evaporation curve 
of Fig. 272. 

In the fall, when the monthly temperature reaches 20 degrees, 
practically all the precipitation occurs as snow; consequently, 
evaporation for temperatures below 20 degrees is no longer 
dependent on precipitation after the ground has been covered 
with snow, but entirely on temperature. Full evaporation, 
corresponding to the given monthly temperature, is usually 
possible throughout the winter. After the temperature rises 
above 20 degrees, in spring, the evaporation again depends 
largely on available moisture, as determined mainly by precipi- 
tation. Nevertheless, a considerable constant evaporation is 
still possible, irrespective of precipitation, because a certain 
quantity of snow and ice is almost always present on the ground 
while the monthly temperature ranges from 20 to 35 degrees. 
After the snow has disappeared, there will still be a relatively 
large constant evaporation, irrespective of the rainfall, unless 
the winter precipitation has been distinctly deficient. 

A gradual reduction in the constant evaporation has been 
assumed for the summer. It is realized, of course, that the 



422 



ELEMENTS OF HYDROLOGY 



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SUPPLEMENTING STREAM-FLOW DATA 423 

constant evaporation during the summer depends, in a measure, 
on the rainfall of each previous month. In making detailed 
computations of evaporation losses, the constant evaporation 
is readily varied by one or two tenths of an inch, in accordance 
with apparent variations in storage. On some watersheds, 
when the fall precipitation is very low and the temperature re- 
mains above 30 degrees, the right-hand portion of the curve is 
used for January and sometimes also for February, that is, 
when the storage is practically exhausted and there is no snow 
on the ground, the constant of evaporation otherwise used 
practically vanishes and the evaporation is entirely proportional 
to the rainfall. In the same way, when the fall rains are copi- 
ous and the ground-water supply is abundant, a constant of 
evaporation one or two tenths higher than that given by the 
curve may be used to advantage. 

The portions of the limiting curve below temperatures of 
approximately 35 degrees represent evaporation from snow and 
ice surfaces. At the higher temperatures the limiting curve 
represents values somewhat less than the evaporation from 
shallow water. The quantity evaporated out of each inch of 
rainfall becomes less and less as the monthly precipitation in- 
creases, varying more rapidly at the lower than at the higher 
rates of precipitation. 

To the values of evaporation, in inches of depth per month, 
as taken off the curve, a coefficient must be applied to reduce 
these quantities to actual evaporation from the given water- 
shed. This coefficient ranges from about .95 to 1.25 for most 
watersheds of the Northwest and for similar ones elsewhere. 
Very sandy watersheds may require a coefficient as low as .60 
and very impervious flat watersheds may require a coefficient 
in excess of 1.25. The coefficient to be used depends on topog- 
raphy, vegetal cover, soil, subsoil, humidity, and wind. An 
extremely high coefficient of evaporation (in excess of 1.25) 
would result from flat topography devoid of vegetation, moder- 
ately pervious, shallow soil underlain with impervious subsoil 



424 ELEMENTS OF HYDROLOGY 

or rock, low humidity, and high wind velocity. An extremely 
low coefficient (less than .95) would result from rugged topog- 
raphy, bare scanty soil underlain with rock, high humidity, and 
low wind velocity or extremely sandy soil. Between these 
limits the usual working values will be found. With a little 
experience, one can select coefficients for different watersheds 
with considerable accuracy. 

The Author's Transpiration Curve. — The base values for 
total transpiration, in inches of depth, during the growing 
season on any given watershed, are selected with reference to 
the character of the vegetation and the length of the growing 
season on that watershed, giving consideration also to available 
sunshine. In the following computations a normal seasonal 
transpiration of about 9 inches has been assumed for small 
grains, grasses and other agricultural crops, 8 to 12 inches for 
deciduous trees, 4 inches for evergreen trees and 6 inches for 
small trees and brush The normal monthly distribution of 
this total seasonal transpiration is based mainly on temperature. 
To obtain actual transpiration in any given month, however, 
the values taken from the transpiration curve, Fig. 164, p. 244, 
after being multiplied by a coefficient, must be further modified 
on the basis of available moisture. Where precipitation minus 
evaporation for a given month is insufficient to meet the normal 
plant requirements for that month, the ground-water is drawn 
on to a varying extent, depending on the character of the root 
system of the given vegetation, the depth and character of the 
soil, and the quantity of surface soil storage, as determined by 
the precipitation minus losses for previous months. 

Synopsis of Author's Method of Computing Annual Runoff 

The main features of the author's method of computing 
runoff to supplement observed stream-flow data may be sum- 
marized as follows: 



SUPPLEMENTING STREAM-FLOW DATA 425 

I. Collection of physical data. 

a. Rainfall and temperature data for stations on and near 
the given watershed from which monthly rainfall and 
temperature for the watershed are estimated. In 
case rainfall data are meager, charts showing iso- 
hyetals for the portion of the State in which the 
watershed is situated are of assistance. 

6. Data relating to wind velocity, relative humidity, and 
any other prominent weather characteristics. 

c. Data relating to topography, vegetal cover, soil, and 

subsoil, as affecting evaporation. 

d. Data relating to character and density of vegetation 

and length of growing season, with reference to tem- 
perature and hours of sunshine. 

e. Data relating to area of open water surfaces, swamps, 

and marshes. 

II. Determination of losses. 

a. Evaporation from water area. 

1. Monthly evaporation corresponding to given temper- 
ature and season, taken off curve, Fig. 150, and 
multiplied by percentage of water surface, based on 
data under I-e, and coefficient based on data under 
1-6. 

6. Evaporation from land area. 

1. Determination of coefficient for given watershed, based 

principally on physical data under I-c and 1-6. 

2. Determination of evaporation, in inches depth per 

month, corresponding to given monthly tempera- 
ture and rainfall for given season of year, from 
curve of evaporation from land areas, Fig. 272, and 
multiplication of this value by percentage of land 
area and coefficient determined under II-6-1. 
c. Transpiration from land area. 

1. Determination of normal seasonal transpiration, based 
on physical data under l-d. 



426 ELEMENTS OF HYDROLOGY 

2. Determination of transpiration coefficient by finding 

ratio between seasonal transpiration determined 
from base curve of transpiration (Fig. 164) for the 
normal monthly temperatures for the given water- 
shed, and the normal seasonal transpiration deter- 
mined under II-c-1. 

3. Determination of monthly transpiration by applying 

transpiration coefficient to monthly values taken 
off transpiration curve for given monthly tempera- 
tures, and modification of these monthly values on 
basis of rainfall, percolation, and storage. 

III. Determination of total loss by summation of monthly 
losses from land and water areas, the deduction of these monthly 
losses from the monthly precipitation, and summation of these 
monthly residuals to give the annual yield of the given water- 
shed, with or without correction of this annual total for fall 
surface runoff, or changes in ground and surface storage. 

IV. Where the annual yield and its distribution throughout 
the year are both desired, additional curves similar to those for 
the Root River watershed, and computations similar to those 
given in Table 43, for the same watershed, must be made. 
When the more detailed computations, as here indicated, are 
carried out, it is possible to make more accurate estimates of 
transpiration during months of deficient rainfall, because more 
accurate values of soil and subsoil storage are available. 

Fig. 273 is a relief map of the United States based on the 
maps published by the United States Geological Survey. Figs. 
27, 28, 29, 67, 180 and 273 are of service in determining the 
evaporation coefficient and Figs. 67, 163 and 168 aid in de- 
termining the normal seasonal transpiration on any given 
watershed. 

Computing Annual Yield. — The author's method of com- 
puting the annual yield in runoff from a watershed will be 
reasonably clear from the preceding synopsis, as the several 
stages are given in considerable detail. Large watersheds 



SUPPLEMENTING STREAM-FLOW DATA 427 




rt 



428 



ELEMENTS OF HYDROLOGY 



should be broken up into smaller units and the yield of each 
computed separately. Table 42 is a summary of the results 
of the application of this method to fifteen widely different 
watersheds. These data show a satisfactory correspondence 
between computed and observed runoff.* Preliminary compu- 
tations of evaporation and transpiration losses are likely to be 
modified somewhat when the monthly runoff is computed. 



TABLE 42. — OBSERVED AND COMPUTED PHYSICAL DATA 
FOR FIFTEEN WATERSHEDS 





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Observed and computed physical data — 
mean annual 


Name of watershed 


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03 

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17 


1 20 


19,500 


27 3 


41 


14 4 


7 7 


22 1 


5 2 


5 23 


5 31 


Little Fork 


5 


1.10 


1,720 


23.9 


37 


11.2 


6.9 


18.1 


5.8 


5.80 
*5.15 


*5.13 




5 


1.25 


6,300 


22.7 


43 


14.1 


7.5 


21.6 


1.1 

'0.77 


1.1 

*0.77 






*0.70 


Root 


6 


1.225 


1,560 


31.4 


45 


16.5 


8.9 


25.4 


6.0 


6.10 
*5.16 


*5.20 


Ottertail 


6 


1.10 


1,310 


23.0 


40 


13.5 


6.6 


20.1 


2.9 


2.80 




St. Croix 


11 


1.05 


5,930 


30.0 


41 


13.1 


7.0 


20.1 


9.9 


f2.66 
9.90 


t2.59 
9.60 


Ohio 


14 


0.875 


23,820 


41.1 


51 


14.8 


5.8 


20.6 


20.5 


20.50 


22.00 


Tohickon Creek. . . 


24 


0.90 


102 


48.9 


51 


16.7 


7.0 


23.7 


25.2 


25.2 


26.10 


James 


7 


0.925 


6,230 


42.1 


54 


16.3 


7.0 


23.3 


18.8 


18.90 


18.00 


Roanoke 


9 


0.90 


390 


42.6 


57 


16.9 


7.0 


23.9 


18.7 


18.60 


17.70 


Tombigbee 


9 


1.05 


4,440 


49.2 


62 


22.8 


8.4 


31.2 


18.0 


18.00 


17.10 


Colorado 


10 


1.20 


37,000 


26.9 


66 


17.7 


8.1 


25.8 


1.1 


1.06 


0.74 


Sacramento 


9 


0.85 


10,400 


32.2 


52 


8.5 


2.4 


10.9 


21.3 


21.3 


20.40 


Pit :.'. 


6 


1.10 


2,950 


14.8 


48 


6.9 


3.0 


9.9 


4.9 

*3.87 


4.9 

*3.S7 


*3.92 


McCloud 


6 


0.60 


608 


61.9 


55 


8.2 


2.4' 


10.6 


51.3 


51.3 


54.00 



Four years' records. 



t Five years' records. 



Computing Monthly Runoff. — It is well to keep in mind, in 
comparing monthly computed stream flow with observed data, 
that both observed and computed runoff data for any given 
watershed are of service only as a basis for estimating the runoff 
which will probably occur in the future. An identical recur- 

* See author's paper "Computing Runoff from Rainfall and Other Physi- 
cal Data," Trans. Am. Soc. C. E., Vol. LXXIX, pp. 1056 to 1224, 1915. 



SUPPLEMENTING STREAM-FLOW DATA 429 

rence of any given combination of meteorological phenomena 
on any one watershed is extremely improbable. In view of 
this fact, the complete daily, and, to a large extent, the monthly 
distribution of runoff, is of much less importance than the 
annual yield of a watershed, the probable extreme maximum 
flow, the extreme minimum and a reasonably accurate estimate 
of runoff below the limit of economical utilization for whatever 
purpose the stream flow is to be used. 

Inasmuch as the low- water flow from most small watersheds 
is so extremely small as to be hardly capable of economical use 
except through storage reservoirs, the sudden fluctuations in 
stream flow below the maximum expected flood, with the reser- 
voir filled, are of little consequence. Whether one inch of 
runoff occurs in a few days or in a few weeks is not of much 
consequence on such a watershed if all the available runoff can 
be held in the storage reservoir for gradual utilization. The 
engineer is usually much more interested in the total runoff 
from such a watershed, up to the point of economical utiliza- 
tion, than in the exact distribution of that runoff through the 
year. 

Ability to compute the monthly distribution of runoff re- 
quires an understanding of all the factors affecting stream 
flow, heretofore discussed. It is also necessary to have rather 
complete data regarding the geological, topographical, and cul- 
tural conditions of the watershed and daily temperature and 
precipitation data. Next, curves of the type shown in Figs. 
274 to 276 for the Root River, Minnesota, must be prepared. 
These curves may be based upon the results of a study of the 
available runoff data for the watershed under investigation or 
for a reasonably similar adjoining watershed, but should prefer- 
ably be checked by at least short-term runoff records for the 
same watershed. 

The curves of Fig. 274 show, in the first place, the approxi- 
mate maximum quantity of snow which, when available, will 
melt at the given monthly mean temperatures. The other 




2 3 4 5 

Inches of Depth on Land Area 

Fig. 274. — Relation between Temperature, Melted Snow, Soil Storage 

and Percolation. 



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ROOT RIVER 

AT 

HOUSTON, MINN. 

















































































































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1 2 3 4 5 

Surface Flow, in Inches per Month 

Fig. 275. — Relation between Residual Precipitation, Soil Storage 

and Surface Flow. 



SUPPLEMENTING STREAM-FLOW DATA 



431 



curves in Fig. 274 give the estimated quantity of this melted 
snow which will percolate into the ground under various con- 
ditions of soil storage. The drier and the more sandy the soil, 
even though frozen, the more melting snow it will absorb. A 
portion of the melted snow which does not percolate into the 
ground will immediately run off into the streams. Another 
portion will be retained for some time, part to appear as runoff 



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ROOT RIVER, MINN. 

AND 

SIMILAR WATERSHEDS 













































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































































0.1 



0.2 0.3 0.4 0.5 0.6 

Seepage Flow-Inches per Month on Drainage Area 



0.7 



0.8 



Fig. 276. — Relation between Sub-soil Storage and Seepage Flow. 

later, and part to be gradually absorbed by the soil. The 
proportion retained for a time depends largely on topographic 
conditions. It may be treated substantially as precipitation 
minus losses for the following month, resulting from well- 
distributed rains. 

The curves of Fig. 275 are to be used to aid in determining 
the quantity of surface runoff resulting from a given monthly 
" precipitation minus losses." Their application necessitates 



432 ELEMENTS OF HYDROLOGY 

the use of daily precipitation records, and allowance must be 
made for concentration and intensity of precipitation during 
the month. In Minnesota, less surface runoff will, in general, 
result from a given " precipitation minus losses " in spring and 
fall than in summer, because the rains are usually well distrib- 
uted during the former seasons. Some latitude must be allowed 
and judgment exercised in the application of these curves. 

On very sandy watersheds the curves of Figs. 274 and 275 
having a value of 2 inches, for example, might have a value of 
3 or 4 inches, and on very clayey watersheds these same curves 
might have a value of 1 inch or even 0. 

The curves of Fig. 276 are to be used to determine the seep- 
age flow for a given quantity of subsoil storage. On the Root 
River watershed moisture which has once passed down through 
the upper foot or two of soil will continue downward, as a rule, 
to join the subsoil storage and aid in maintaining stream flow. 
It is practically safe against return through the action of 
capillarity. 

Two curves are given in Fig. 276, one for Lanesboro where 
the watershed area is 615 square miles and one for Houston 
where the watershed area is 1560 square miles. These curves 
have been applied to other watersheds in southeastern Minnesota 
and are applicable to similar watersheds elsewhere. The shape 
of similar curves for other watersheds depends mostly upon the 
topography, the character of the soil and subsoil, and the size 
of the drainage basin. 

In order to show the application of the writer's method of 
computing the monthly distribution of annual runoff, the de- 
tailed computations for the Root River watershed at Houston, 
Minn., are given in Table 43. 



SUPPLEMENTING STREAM-FLOW DATA 



433 



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436 i ELEMENTS OF HYDROLOGY 

Summing up the monthly runoff figures, as computed in this 
way, gives a value for the annual runoff which is much more 
accurate, and differs somewhat, from the computed annual 
" precipitation minus losses." 

On watersheds such as that of the Colorado River in Texas, 
where the precipitation is distributed throughout the year in a 
similar manner to that prevailing throughout the Northwest, but 
where temperatures are so high that evaporation losses absorb 
by far the greater portion of the rainfall, and where the de- 
mands of vegetation for moisture are never fully supplied, 
practically all of the stream flow consists of surface runoff. On 
these watersheds, where there is no well-defined water-table 
above the stream bed, the entire runoff results from heavy 
rains, commonly called " cloudbursts," over small areas. As 
the surface of the ground on such watersheds is usually very 
dry, percolation is not very rapid; hence some of the rainfall 
escapes over the surface of the ground as runoff before sufficient 
time has elapsed for it to be evaporated, or to be used by vege- 
tation. On such watersheds the character of the soil is the 
principal factor determining the amount of runoff. This is well 
exemplified by the discharge records of the Smoky Hill, the 
Saline, the Republican, and the Loup Rivers in Kansas and 
Nebraska. 

As the runoff from watersheds of this character is usually 
very small the results of computations are certain to be in error 
by a large percentage even though the absolute error in inches 
depth may be very small. The same criticism applies to short- 
term observations of stream flow on such watersheds. As the 
flow of streams draining these watersheds is dependent upon 
heavy rains, the irregularities in stream flow are always great. 
If the watershed is sandy the underflow may constitute a far 
more dependable water-supply than the surface flow of the 
streams. 



CHAPTER XII 

MODIFICATION OF STREAM FLOW BY STORAGE 

Applicability Dependent Upon Cost 

The extent to which stream flow can be modified by the 
storage of water is primarily dependent upon the relation be- 
tween the quantity of water which must be controlled in order 
to produce the desired modification in flow and the oppor- 
tunities for reservoir construction. This relation is well stated 
by Van Ornum * in the following words: 

" For example, a billion cubic feet of stored water 
will supply a city of one or two hundred thousand in- 
habitants for a year; or it will irrigate from 4000 to 
10,000 acres of arid land for a season ; or it will furnish 
more than a million horse-power-hours under a head of 
40 feet; but it would double the volume of low-water 
flow of the Mississippi River at St. Louis for less than 
eight hours, and is exceeded by the flood discharge at 
the same place in one-quarter of an hour." 
The practicability of reservoir construction for any given 
purpose is usually determined by the unit cost of storage. 
Often, however, a projected storage may be economical for a 
given purpose but so much more valuable for another as to 
make it desirable to give the latter object priority and to de- 
pend only upon incidental benefits to the former object. The 
unit cost of water stored in the large reservoirs of the world 
differs greatly, varying from a minimum of $5 per million cubic 
feet, estimated as the cost of storing 168 billion cubic feet on 
the Upper Ottawa River watershed, to $30,000 per million 

* Van Ornum, J. L., The Regulation of Rivers, 1914, p. 57. 
437 



438 ELEMENTS OF HYDROLOGY 

cubic feet as the cost of storing a half-billion cubic feet on the 
Wien River watershed for protecting the City of Vienna from 
destructive floods. The Upper Mississippi River navigation 
reservoirs, with 98 billion cubic feet capacity, cost about $18 
per million cubic feet, and the Ashokan, New York City, water- 
supply reservoir, with a capacity of 17.65 billion, cost $718 per 
million. The reservoirs of Germany, constructed largely in the 
interests of navigation, cost from $500 to $1500 per million 
cubic feet of capacity.* 

Reservoir Sites 

Among the factors determining the desirability of reservoir 
sites are: 

1. Location of site with respect to locality served. 

2. Dependability of water-supply. 

3. Character of reservoir bed and banks. 

4. Character of site for impounding dam. 

5. Effective depth of reservoir. 

The relative importance of these factors depends mainly upon 
the purpose which the reservoir is to serve. 

Location. — The first characteristic of a good reservoir site 
is, of course, a location as convenient as possible to the locality 
that is to be served, whether that service is for water-supply, 
water-power, navigation, irrigation, or for any one of the other 
purposes for which storage reservoirs are useful. 

Water Supply. — Perhaps second in importance is a depend- 
able water-supply. Seepage and evaporation losses are com- 
paratively uniform, definite quantities for which allowance can 
be made in the scope of the project; but an unreliable and 
indefinite supply of water represents a great economic handicap. 
Lender such conditions, provision must be made, in the struc- 
tural features of the project, for both extremes of water-suppfy, 
with the consequent increase in cost and fixed charges. Spill- 
way capacity must be provided so that exceptional flood inflow 
* Van Ornum, J. L., The Regulation of Rivers, 1914, Chapter 1. 



MODIFICATION OF STREAM FLOW BY STORAGE 439 

into the reservoir can be wasted without endangering the sta- 
bility of the impounding structures. On the other hand, suffi- 
cient storage capacity must be provided to furnish the necessary 
water-supply in years, or even a series of years, of exceptionally 
low inflow. For the same reason that, in a given region, a 
small stream usually experiences greater irregularity in flow 
than a large one, a reservoir with a small tributary watershed 
has a more irregular and less dependable water-supply than one 
with a large tributary area. In other words, in any given 
region, a large storage project is usually more dependable than 
a small one. 

Seepage and Evaporation Losses. — For any given water- 
supply, that reservoir whose bed and banks are most nearly 
impervious and whose depth is greatest, will suffer the smallest 
seepage and evaporation loss. For a given temperature, evapo- 
ration from the water surface of a reservoir is directly propor- 
tional to its superficial area. The percentage of stored water 
lost in evaporation, then, except for small changes in reservoir 
area with stage, is inversely proportional to the depth of the 
reservoir. An increase in the depth of water in a reservoir, 
however, results in a decrease in its temperature and, hence, 
in a decrease in evaporation loss per unit of area. 

Seepage losses from a reservoir are dependent upon the 
character and the dip of the strata of material that constitute 
its bed and banks, and on the elevation of the water-table in 
the given locality. In the United States east of the Mississippi, 
reservoir sites are almost invariably located in natural depres- 
sions that have the water-table close to the surface of the 
ground. Moreover, in this region, the water-table in the bor- 
dering hills usually slopes toward the reservoir site. Under 
such conditions seepage losses are usually negligible, and some 
of the percolating water returns to the reservoir as seepage 
flow when the stored water is being withdrawn. In arid and 
semi-arid regions, on the other hand, the water-table is so 
far below the level of the ground that seepage losses from reser- 



440 



ELEMENTS OF HYDROLOGY 



voirs usually amount to from 15 to 30 per cent of the entire 
supply. In such regions, the character of the reservoir bed and 
banks is far more important than when the water-table is high, 
and may overshadow in importance even the character of the 
site for impounding structures. Observed seepage and evapo- 
ration losses from a typical western reservoir are shown in Fig. 
277.* On most western reservoirs seepage reduces with time 
on account of the raising of the water-table and the silting up 
of the porous bed and banks. In some instances, clay may 
be sluiced into the reservoir to reduce seepage losses. This has 
been proposed for the Cedar Lake Reservoir, Washington, f 




Dee. Jan, 
1910 



JTeb. Mar. Apr. May June July Aug. 
COLD SPRINGS RESERVOIR, ORE. 



Sept. Oct. Nov. 
1911 




Mar. Apr. May June July Aug. Sept. 

UMATILLA PROJECT, ORE. 

Fig. 277. — Seepage and Evaporation Losses from Typical Western 
Reservoir and Canal System. ^ 



Spillway Capacity. — The storage of water necessitates the 
use of impounding structures equipped with facilities for the 
discharge of excess water in time of extreme flood. Water that 
is available only once in ten, fifteen, or twenty years is not 
only useless but constitutes a source of danger. The history 
of wrecked dams and embankments in all parts of the country 
bears emphatic witness to its destructive powers. 

* From a paper by E. G. Hopson, Trans. Am. Soc. C. E., 1913, p. 336. 
t Engineering Record, Aug. 19, 1916, p. 228. 



MODIFICATION OF STREAM FLOW BY STORAGE 441 

Dam Site. — A good dam site should provide good founda- 
tion material, preferably rock, and sufficient width to permit 
the installation of ample spillway capacity but no more. Where 
the construction of long earth embankments must be resorted 
to, the presence of clayey material and water, for the con- 
struction of the embankment by the hydraulic process, adds 
to the value of the site. The best sites are usually afforded by 
steep, narrow canyons, with rock bed and banks, which permit 
the construction of arch masonry dams, and the discharge of 
flood water without endangering the structure through erosion 
of the river bed on the downstream toe. 

Sedimentation of Reservoirs. — While the possibility of the 
gradual reduction of reservoir capacity through the deposition 
of the silt carried by tributary streams must receive due con- 
sideration in each project, the danger of the silting up of reser- 
voirs is usually negligible. Few artificial reservoirs are ever 
drained dry and natural lakes which are utilized in reservoir 
construction have such great storage capacity below the low- 
water level that the silting of centuries could hardly have an 
appreciable effect. The substantially unchanged existence of 
natural lakes in all parts of the world bears witness to this fact. 
Stabler * estimates that the system of reservoirs proposed for 
the Ohio River might silt up to the extent of 10 per cent of 
its capacity in about 800 years. Under exceptional conditions, 
however, an artificial reservoir may silt up quite rapidly as 
indicated by the Tuolumne River Reservoir at La Grange, 
Cal. The amount of silting which may be expected in a given 
time is directly proportional to the sediment carried by the 
tributary streams and the ratio of tributary watershed to 
reservoir area. 

Effectiveness of Reservoir Storage 

Losses in Conveying Channels. — When stored water is dis- 
charged from reservoirs and conveyed to the point of utilization 
* Stabler, Herman, Engineering News, 1908, Vol. 60, p. 649. 



442 



ELEMENTS OF HYDROLOGY 



through rocky channels, concrete-lined tunnels or canals, steel 
pipes or similar impervious conveyors, the losses are negligible, 
or limited to evaporation from the whole or part of the exposed 
surface, and all, or nearly all, of the reservoir discharge may 
be considered as effective. On the other hand, when stored 
water is discharged through natural or artificial channels with 
earth bed and banks the effective portion of the reservoir dis- 
charge may be relatively small. If the water-table lies below 
the channel, whether natural or artificial, the seepage loss is 
usually large. The principal factors influencing this loss are 
the character of the material constituting the bed and banks 
of the channel and the wetted perimeter of the channel. An- 
other factor of more or less importance in different instances 
is the presence of vegetation on the banks of the channel and 
on the water surface itself. In a channel in which these three 
factors are constant an increase in the velocity of the water 
will reduce the percentage lost in seepage. When the velocity 
is increased, however, to a point .where sedimentation is pre- 
vented and scouring results, no further economy is effected. 



TABLE 


44. 


-SUMMARY OF 

MENTS 


323 SEEPAGE 

(Fortier) 


MEASURE- 


Capacity 


of canal, 


sec. -ft. 






Number of 

tests 


Average loss per mile, 
per cent * 


Less than 1 

1 to 5 


16 
37 
30 
49 
48 
31 
26 
45 
87 
14 


25.7 
20.2 


5 to 10 . 


11.7 


10 to 25 


12.1 


25 to 50 


5.5 


50 to 75 


4.3 


75 to 100 


2.7 


100 to 200 

200 to 800 

800 and over 


1.8 
1.2 
1.0 



* Loss per mile in per cent of total flow. 

For typical soils of the arid region, consisting of about 16 
per cent clay, 36 per cent silt, 19 per cent very fine sand and 
18 per cent of fine sand, by volume, Fortier * gives the following 
* Fortier, Samuel, Eng. News, 1915, Vol. 73, p. 1060. 



MODIFICATION OF STREAM FLOW BY STORAGE 443 

average observed seepage losses in canals. The depth of the 
smallest ditches listed in this table varied from 2 to 4 inches 
and of the largest canals from 5 to 8 feet. 

Loss through Temporary Ground-water Storage. — If the 
water-table lies above the channel, some of the discharged 
water will be temporarily lost through seepage. The effective 
portion is difficult to determine. 

During the low-water seasons the stream flow, which it is 
desired to increase through the discharge of stored water, al- 
most invariably consists entirely of seepage flow derived from 
the ground-water supply. Each succeeding reduction in river 
stage tends to maintain the prevailing slope of the ground- 
water surface toward the river channel, with a consequent 
continuation in flow of ground- water into the stream. If, now, 
the river stage be suddenly raised, or prevented from falling, 
through the discharge of stored water, the slope of the ground- 
water surface toward the stream will be reduced or even tem- 
porarily reversed and, hence, the discharge of seepage water 
retarded. This fact is well illustrated by Fig. 278.* This 
figure shows the elevation of the water-table at Muscatine, 
Iowa, for 3000 feet back from the Mississippi River during 
a rise and fall in river stage of about 9 feet. The material 
which constitutes the valley floor, and in which the ground-water 
table lies, consists of sand and fine gravel. Notwithstanding 
this fact, however, the changes which occurred in the level of 
the water-table, in this distance of 3000 feet, occupied several 
weeks. There were very heavy rains in the vicinity during 
the first two weeks of September, and light rains to October 
6 to 7. Apparently the rains of September 1 to 15, amounting 
to about 5 inches in the vicinity of Muscatine, caused a rise 
in the water-table, as the result of percolation, approximately 
equal to the small rise in river stage. Then, from September 
16 to 27, there was a pronounced rise in river stage accom- 

* Hubbard, W. D., and Kiersted, W., Waterworks Management and 
Maintenance, 1907. 



444 



ELEMENTS OF HYDROLOGY 







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S .2 



MODIFICATION OF STREAM FLOW BY STORAGE 445 

panied by only a small rise in the water-table. From Sep- 
tember 27 to 30 the water-table rose almost as fast as the 
river, and continued to rise from that date until October 12, 
while the river was falling. 

Retardation of Seepage Flow. — The extent to which the 
increase in river stage, resulting from the discharge of stored 
water from reservoirs, tends to retard seepage flow, and to 
defeat the object of reservoir discharge by temporarily wasting 
the water in replenishing the ground-water supply adjacent to 
the river channel, cannot be determined from the data at pres- 
ent available. Some of the factors influencing the extent of 
such action may, however * be considered. Perhaps the most 
important single factor is tue length of river channel affected 
by the rise in stage caused by the reservoir discharge. A num- 
ber of small reservoirs at the headwaters of different tributaries 
would affect a much greater length of channel than a single 
large reservoir on a single tributary. Streams deriving their 
seepage flow from a coarse, sandy or gravelly subsoil are af- 
fected more than those deriving their seepage flow from the 
finer sands or sand rock. Streams flowing in deep valleys 
through rolling country are relatively less affected than those 
flowing in shallow channels through comparatively flat land. 

The seepage flow of Minnesota streams, during ordinary low- 
water years, amounts to about .3 inch in depth over the drain- 
age area, per month. A reduction in flow from .3 inch to .1 
inch per month on these streams would represent a lowering 
of the ground-water-table over the tributary watershed of 
about 1 or 2 feet. If the river stage is prevented from falling, 
a large portion of the ground- water adjacent to the. channel 
will be prevented from reaching the stream, and the rate of 
flow from the remainder of the watershed subject to the direct 
influence of river stage will be reduced. As the effect of in- 
creased river stage, however, is limited to the channel through 
which the reservoir water is being discharged, and to the lower 
reaches of its tributaries, the retardation in seepage flow is 



446 



ELEMENTS OF HYDROLOGY 



similarly limited to the local drainage area of the main stream and 
the lower reaches of its tributaries. The probable effect in each 
instance must be estimated on the basis of the best available data. 



20,000 



20,000 







Fig. 279(a). — Effect of Upper Mississippi River Reservoirs on Stream 
Flow at Minneapolis, Minn. 



MODIFICATION OF STREAM FLOW BY STORAGE 447 




Fig. 279(b). 



• Effect of Upper Mississippi River Reservoirs on Stream 
Flow at Minneapolis, Minn. 



448 



ELEMENTS OF HYDROLOGY 



20,000 

19,000 

18,000 

17,000 

16,000 

!»15,000 

fa 

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CD 13,000 

be 

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11,000 
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4,000 

3,000 

2,000 

1,000 



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19,000 
18,000 
17,000 
16,000 
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14,000 d 
13,000 g, 

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10,000 <-> 
9,000 2 
8,000 g 
7,000 « 

a 

6,000 as 

5,000 8 

4,000 

3,000 

2,000 

1,000 



4,000 
3,000 



2,000 



fa 



279 (c). — Effect of Upper Mississippi River Reservoirs on Stream 
Flow at Minneapolis, Minn, 



MODIFICATION OF STREAM FLOW BY STORAGE 449 

If the discharge of stored water is continued from one freshet 
to the next, the resulting retardation of seepage flow will reduce 
the available ground storage capacity and thus, to a very lim- 
ited extent, affect the height of the succeeding freshet. On 
northern streams summer discharge from reservoirs will increase 
seepage flow during the following winter to the extent of the 
discharge that was lost in seepage during the summer. The 
effect on stream flow, of course, will be a maximum immedi- 
ately after the reservoir discharge ceases. Slight indications 
of such reappearances of seepage loss appear in the data of 
Fig. 279 for the Upper Mississippi River reservoirs. 

Evaporation Loss in Channels. — The evaporation loss from 
reservoirs discharging through natural channels is usually neg- 
ligible. Such loss is limited to the evaporation from the in- 
creased width of the stream, resulting from the increased stage. 
Only in rare instances does the discharge of stored water from 
reservoirs result in increasing the width of the conveying chan- 
nels by more than a few per cent. In the case of artificial 
channels, of course, the evaporation loss from the entire water- 
surface must be deducted from the reservoir discharge in de- 
termining the effective portion. 

Other Factors. — Other factors deserving consideration in 
determining the effectiveness of reservoir discharge in par- 
ticular instances will be discussed in connection with the several 
purposes for which stored water is used. 

Storage for Municipal Purposes 

For Water-supply Purposes. — The storage of water which 
is most far-reaching in its effects is storage for municipal pur- 
poses. A great many municipalities are entirely dependent 
upon stored water for their municipal water-supply. Promi- 
nent among these are New York and Boston on the Atlantic 
Coast, and San Francisco and Los Angeles on the Pacific. As 
the quantities of water ordinarily required for domestic con- 
sumption are relatively small, the provision of the necessary 



450 ELEMENTS OF HYDROLOGY 

storage capacity is entirely practicable. Greater New York, for 
example, with its millions of people and all its manufacturing 
establishments uses about 1000 cubic feet of water per second. 

As the low-water supply is often insufficient even to balance 
the evaporation from the reservoir surface, it is not unusual 
for municipal water-supply reservoirs to control the entire 
ordinary runoff from the tributary watershed, and to effect 
equalization of flow over a period of several years. McCulloh* 
states that the runoff from the Croton River watershed, New 
York, is so thoroughly controlled that nine tenths of the entire 
yield is utilized. A comprehensive paper entitled " Storage to 
be Provided in Impounding Reservoirs for Municipal Water 
Supply " by Allen Hazen, in which the law of probabilities 
is applied to the storage problem, appears in Vol. LXXVII, 
p. 1539, Trans. Am. Soc. C. E. 

For Improving Sanitary Conditions. — The release of stored 
water to increase the low-water flow is also effective in improv- 
ing the sanitary condition of streams into which relatively large 
quantities of sewage are being discharged. Similarly, a re- 
duction in hardness and acidity may be secured in the case 
of streams into which mine drainage and manufacturing wastes 
are being discharged in large quantities. At low-water stage 
the Monongahela River at Pittsburgh, for example, is so acid, 
primarily as the result of mine drainage, that carbon steel 
plates on lock gates become badly corroded in two years, and 
even nickel-steel plates last only about four years. t Unsanitary 
conditions prevail on many eastern streams. A typical project 
for the improvement of these conditions is that proposed for 
the Naugatuck River, Conn. J Three reservoirs with a com- 
bined capacity of 1.75 billion cubic feet are proposed for the 
purpose of increasing the extremely small low-water flow of this 
stream which has virtually become an open sewer. 

* McCulloh, Walter, Conservation of Water, p. 61. 
t Report of Pittsburgh Flood Commission, p. 248. 
t Engineering Record, Apr. 29, 191G, p. 573. 



MODIFICATION OF STREAM FLOW BY STORAGE 451 

Storage for Irrigation 

The Committee of the American Society of Civil Engineers 
on "A National Water Law " in its preliminary report of 
January, 1916, places the use of water for crop production next 
in importance to its use for household purposes. With this 
view, the author is in accord. No other use of water can yield 
an equal return in the necessaries of life. 

Aside from the small irrigation systems connected with truck 
farms in the East, irrigation projects involve large expenditures 
of money and the storage of large quantities of water. Under 
the direction of the Federal Reclamation Service irrigation has, 
in recent years, made great progress. The third largest reser- 
voir in the world, that at Elephant Butte, New Mexico, with 
a capacity of 115 billion cubic feet, is among the great reser- 
voirs built by the Reclamation Service for the storage of water 
for use in the irrigation of arid lands. 

On account of the large evaporation and seepage losses from 
reservoirs and canals and in the irrigated fields themselves, 
large quantities of water must be stored on irrigation projects. 
As the need for irrigation is an indication of insufficient or 
ill-timed precipitation, and as in such regions the low-water 
flow of streams is usually previously appropriated and used, 
dependence must be placed on flood-water storage. 

For storage purposes the flow of northern streams that rise 
in the mountains and are snow-fed is more dependable than 
that of more southern rain-fed streams. The freshets occur 
later on northern streams, and consequently there is less evapo- 
ration loss after storage. Freshets on rain-fed streams are very 
irregular, and usually occur early in the season. 

As most rivers in the arid and semi-arid regions decrease in 
volume, through percolation and evaporation, as they spread 
out upon the plains, the best storage sites are in the upper 
valleys. Here the water-table is usually above the stream-bed, 
good dam sites are available, and by storing water to con- 



452 ELEMENTS OF HYDROLOGY 

siderable depth, the evaporation losses from the reservoir are 
greatly reduced. 

Seepage from irrigation reservoirs and canals, and from irri- 
gated fields, is manifesting itself in the increase of the low- 
water flow of streams in these regions and in the necessity for 
the drainage of low-lying lands. 

Although considerable power is being developed on a number 
of irrigation projects, such use of the stored water is entirely 
secondary to its use for agricultural purposes. 

Storage for Logging 

One of the most extensive uses of stored water in the modi- 
fication of stream flow is in connection with logging operations. 
Although the quantity of water stored in connection with each 
project is usually small, logging dams abound wherever logging 
operations are carried on. As the sluicing of logs is usually 
completed by midsummer, the stored water does not help to 
increase the late summer low-water flow. When logging dams 
are located in out-of-the-way places, the gates are usually 
closed in the fall so as to insure a good supply of water for the 
succeeding season. Such operation inevitably reduces the 
winter low-water flow and increases the spring high-water. 

Storage for Navigation 

Applicability. — The storage of water on navigable lakes for 
the maintenance of better stages on these lakes, and also the 
storage of water for feeding navigable canals, as in Lake Gatun, 
for example, has been successfully performed by different 
nations for many years. The increase of river stages through 
the discharge of stored water, however, has very limited appli- 
cation on account of the tremendous quantity of water required 
to effect substantial increases in stage on the lower, navigable, 
reaches of the streams. The discharge from storage reservoirs 
has less and less effect, in increasing river stages, progressively 
downstream. Usually the only feasible reservoir sites are 



MODIFICATION OF STREAM FLOW BY STORAGE 453 

located near the headwaters of the streams. Where the effect 
is greatest, the stream is usually not navigable and when the 
navigable reach of the main stream is reached, the effect of 
reservoir discharge is usually very small. In portions of 
Europe where the streams are relatively short, water storage 
for increasing navigable stages has found some application, but 
nearly all projects applicable to the larger streams, both in 
Europe and in the United States, have been unfavorably re- 
ported upon. In Germany, where the greatest development 
of storage in the interests of navigation has taken place, no 
system of reservoirs used has a greater capacity than about 
10 billion cubic feet. This naturally limits their effect to 
reaches of not more than two or three hundred miles of river. 

The Two Largest Navigation Reservoirs. — There are two 
large reservoir systems in the world constructed and operated 
solely in the interests of navigation. The oldest of these sys- 
tems is that in Russia, with a capacity of 35 billion cubic feet. 
The effect of this system of reservoirs is substantially limited 
to the 300 miles of river immediately below the reservoirs. 

The largest system of reservoirs in the world constructed 
in the interests of navigation is the Upper Mississippi River 
system in Northern Minnesota. The combined capacity of the 
six reservoirs constituting this system is nearly 98 billion cubic 
feet. This is sufficient to store twice the average annual runoff 
from the tributary watershed. 

Effectiveness of Navigation Reservoirs. — Fig. 279 shows the 
total amount of water stored in these reservoirs at the end of 
each month for the past 12 years, together with the monthly 
change in storage expressed in cubic feet per second, the monthly 
mean discharge from the reservoirs, and the discharge of the 
Mississippi River at the site of the Government Dam now 
under construction in the Twin Cities. 

Table 45 shows the percentage of the total reservoir capacity 
that was utilized each year, together with the maximum and 
minimum storage and the month in which this occurred. 



454 



ELEMENTS OF HYDROLOGY 



TABLE 45. — STORAGE UTILIZED EACH YEAR IN THE 
UPPER MISSISSIPPI RIVER RESERVOIRS 



Year 


Maximum quantity in storage 
during year 


Draft on storage after filling reservoir 


Date 


Billion 
cu. ft. 


Billion 
cu. ft. 


Percentage 
of total 
capacity 


Date of maximum draft 


1905 


August 1 


81.6 


28.3 


29 


April 1, 1906 


1906 


July 1 


71.0 


19.8 


20 


April 1, 1907 


1907 


July 1 


66.8 


19.3 


20 


December 1, 1907 


1908 


July 1 


73.0 


23.6 


24 


February 1, 1909 


1909 


September 1 


66.8 


5.6 


6 


March 1, 1910 


1910 


May 1 


65.5 


35.0 


36 


February 1, 1911 


1911 


June 1 


42.2 


14.9 


15 


December 1, 1911 


1912 


June 1 


39.5 


19.4 


20 


March 1, 1913 


1913 


August 1 


37.9 


7.9 


8 


October 1, 1913 


1914 


July 1 


57.4 


7.0 


7 


September 1, 1914 


1915 


August 1 


80.2 


21.4 


22 


March 1, 1916 


1916 


July 1 


90.1 













The storage of water during the early spring and its release 
in the interest of navigation during the summer low-water 
period is very apparent. It will also be noted, however, that 
very little water is discharged during the winter low-water 
period when there is the greatest demand for water-power and 
when the stream flow is the lowest, but that, on the contrary, 
some water is often stored during the winter months. 

The discharge of stored water during the summer low-water 
months of exceptionally dry years, such as 1910 and 1911, has 
a marked effect on the stage of the upper 175 miles of navigable 
stream immediately below the three principal reservoirs. The 
commerce on this portion of the river is, however, extremely 
small. The next 150 miles of river, to the center of Minne- 
apolis, are given over to power development and are not navi- 
gable. From Minneapolis and Saint Paul to Lake Pepin, a 
distance of about 70 miles, the effect of reservoir discharge 
is to increase the stage, during exceptionally dry years, from 
about 2 feet to practically nothing.* The effect on the stage 
of the remaining 2000 odd miles of the Mississippi River is, for 
practical purposes, negligible. Moreover, the increase in stage 

* Final Report, National Waterways Commission, 1912, p. 193. 



MODIFICATION OF STREAM FLOW BY STORAGE 455 

does not measure the increase in ruling depth. According to 
General Bixby, former Chief of Engineers, U.S.A. : * 

" On the Upper Missouri, within the limits of North 
and South Dakota, while there is often 3.5 to 5-foot 
draft at dead low water, there is only a draft of 3 feet 
at a 5-foot stage of water, the crest of bars rising with 
rising water. On the Mississippi River from St. Louis 
to Red River, where the natural unimproved depth 
over the bars is only about 4 feet, the rise of bar crests 
is about one-half the rise of the river, giving below 
St. Louis only 14 feet on the bars at a 20-foot stage 
above low water so that the benefit to navigation is 
rather illusory." 
Furthermore, the increased stage in the Mississippi River 
between St. Paul and Lake Pepin is of value only when the 
ruling depth for boats coming upriver does not occur below 
Lake Pepin. It is evident that unless up-bound boats can 
reach Lake Pepin the increased stages in the river above that 
lake have little commercial value. 

Storage for Flood Prevention 

Applicability. — The applicability and the limitations of the 
storage of water for flood prevention purposes are determined 
by the causes and the characteristics of the floods of each given 
stream. This fact will be appreciated from the previous dis- 
cussion of precipitation and the hydrographs of floods on typi- 
cal streams. On some streams of the country floods occur in 
winter; on others in spring, summer or fall. A great flood 
may be preceded by one of ordinary magnitude or two great 
floods may follow each other within a relatively few days. To 
be effective, then, flood water must be stored only temporarily 
lest the storage capacity be unavailable when most required. 
Storage capacity that is utilized for holding water over from 

* Bixby, Gen. W. H., Final Report National Waterways Commission, 
1912, p. 193. 



456 ELEMENTS OF HYDROLOGY 

one year to the next cannot be said to be available for flood 
prevention purposes. 

Methods. — Three principal methods are in use for tempo- 
rarily storing water in order to reduce the flood flow of streams. 
Two of these methods are entirely automatic in operation and 
accomplish their object either through the utilization of check 
dams or through " retarding " or " detention " basins. The 
other method employs impounding reservoirs with manually 
operated gates for discharging the stored water at will. 

Check Dams. — Check dams of the type used for preventing 
erosion and floods in the mountainous regions of Austria, Japan, 
and Switzerland are now being tried out in California in a 
region where the rivers fall about 6000 feet in 40 miles and 
carry a great deal of gravel, sand, and silt, which is deposited 
in the form of debris cones whero the streams issue from the 
canyons.* 

The object of check dams is to retard the flow of water down 
the ravines and canyons that comprise the upper watersheds 
of torrential streams, thus reducing erosion, and to encourage 
the greatest possible absorption of water in the ravines them- 
selves, and in the debris cones at the mouths of the canyons. 
Check dams are relatively small, simple, and inexpensive, being 
constructed mainly of loose rock. Typical dams built in Cali- 
fornia under the direction of Olmsted f are shown in Fig. 280. 
Most of the experimental work is being done in Haines Canyon, 
which drains an area of 1.45 square miles of burnt-over, moun- 
tainous land. Although in 1914 this canyon yielded 712 
second-feet per square mile, which is the highest unit runoff 
ever recorded in southern California, the heavy rains of Jan- 
uary, 1916, after the construction of 384 small check dams 
at an average cost of about $12 each, yielded only 113 second- 
feet per square mile as compared with much larger unit yields 

* Engineering News, Feb. 10, 17, and Mar. 23, 1916; Engineering Rec- 
ord, May 13 and 20, 1916. 

t Olmsted, F. H., Consulting Engineer, Los Angeles, Calif., Member of 
Los Angeles Flood Commission. 



MODIFICATION OF STREAM FLOW BY STORAGE 457 

from larger, untreated watersheds in the same locality. The 
extent to which these experimental check dams have increased 
the absorption of water is indicated by the growth of vegetation 
in the canyons and the fact that canyons which were previously 
dry at low water are now yielding a small low-water flow. 




Courtesy Engineering Record. 

Fig. 280. — Typical Check Dams. 



While check dams are unquestionably effective aids in the 
control of flood runoff from small precipitous watersheds where 
the rock does not lie close to the surface of the ground, the 
quantity of water which can be controlled in this way is com- 



458 ELEMENTS OF HYDROLOGY 

paratively small so as to severely restrict the applicability of 
these dams for flood prevention purposes. 

Retarding Basins. — Retarding or detention basins are some- 
what similar in their action to check dams but of much larger 
size and of wider applicability. The first projects in the United 
States employing retarding basins on a large scale are those for 
the protection of the Miami and the Franklin County Con- 
servancy Districts from the floods of the Miami and the Scioto 
rivers in Ohio. Typical cross-sections of the dams proposed 
for the retardation of extreme floods on these streams are shown 
in Figs. 281 and 282. Retarding basins act in a manner essen- 
tially similar to that exemplified by the action of natural lakes 
in that no definite limit is placed, either for the stage which 
water in the basin may reach or the maximum rate of outflow 
from the basin. Both are entirely dependent upon, and in- 
crease with, the magnitude of the flood inflow. In contrast 
with most natural lakes, however, no permanent storage of 
water is provided for and the fluctuations in stage and outflow 
are very rapid. The intention is to permit all ordinary floods 
to pass through the controlling dams unhindered and to merely 
retard or detain rather than to impound the water of extreme 
floods. In consequence the land within the basin may be used 
for agricultural purposes but no buildings nor other improve- 
ments should be permitted within the basin. As indicated in 
Fig. 281 the discharge openings in the dams are carefully pro- 
tected by barriers to prevent their being clogged by floating 
debris, and ample, free spillway capacity is provided, in addition 
to the openings through the base of the dams, to prevent the 
possibility of the overtopping of embankments at times of un- 
precedented floods. The action of a retarding basin in taking 
off the crest from a serious flood is well shown in Fig. 283. 
Since the reduction of flood peak and retardation of flood water 
result in prolonging the flood flow from the basin, thus pro- 
ducing considerably higher than natural stages in the tributaries 
for several days after the natural flood peak, the effect of re- 



MODIFICATION OF STREAM FLOW BY STORAGE 459 

tarding basins on the floods of the main stream into which 
these tributaries feed should always be studied. This is par- 
ticularly necessary in those instances where the retarding basins 
occur on the lower tributaries of a stream lying in a region 




rDDnDnDDDDDDODGDnDonnnncDCCDncnoncnrrcnnnc 

iDDDDnDDnnpnnrnrnnnr.crnrr.nnnrnornnnnr 

tnnnrrn r rr r r rrrr rrr rr.rrnrni 




CHANNEL PIER 



CABLE DRIFT BARRIER 



Anchor Rods 
ENLARGED DETAILS AT A 



105 Diaro.- 




K1J72.0 i i - l w q o * i a, c^^j ^ o \ 



From Report of Alvord and Burdick, Franklin County Conservancy District. 

Delaware Basin on Olentangy River, Tributary of Scioto River, Ohio. 

Fig. 281. — Drift Barrier, Weir and Outlet Conduit of Typical 
Retarding Basin. 



in which the flood-producing rainstorms pass upstream, and 
also, on the other hand, in some instances in which the retard- 
ing basins occur on the upper tributaries of the main stream 
and the flood-producing rainstorms travel downstream. 



460 



ELEMENTS OF HYDROLOGY 




tf 



H 



o 



fa 



MODIFICATION OF STREAM FLOW BY STORAGE 461 



80,000 



g 50.000 



80,000 





f\ 
























1 I 


looH like 
larch 1913 








































(Max. elev. water surface. SJ» 
J • • outflow 32.000 second li. 






\ 


1 


• • storage 124,000 acre fiat 
> • area flooded 7300 acraa 




/ 


































Out 


flo\i 
































<2i» 


•25> 


■Q6* 


Ian 


«28» 


«89> 
313 


«30* 


«31> 




rill 


1*3*1 
913 



From Report of Arthur E. Morgan, Miami Conservancy District. 
Proposed Huffman Basin on Miami River. 

Fig. 283. — Action of Typical Retarding Basin in Taking Crest off Flood. 



Impounding Reservoirs. — The more permanent storage of 
flood water in impounding reservoirs, from which it can be 
released at will, is usually more expensive in both construction 
and operation than more temporary storage in retarding basins. 
Where impounding reservoirs are used, an attempt is usually 
made to conserve and utilize at least some of the stored water 
for increasing the low-water flow. This, however, necessitates 
the permanent withdrawal of flowage lands from agricultural 
use, and constant attendance at the dams. Unless it is strictly 
understood that the reservoir capacity provided for the storage 
of flood water shall not be utilized for permanent storage, such 
combination of storage purposes usually results in an ultimate 
defeat of the object for which the reservoirs were built. To 
be effective for flood prevention, reservoirs must be kept as 
nearly empty as possible. 

From the very nature of their use, flood-prevention reservoirs 
are extremely limited in scope. They are applicable only to 



462 ELEMENTS OF HYDROLOGY 

small watersheds of a few thousand square miles in area, the 
flood runoff from which reaches the streams a few hours after 
the rains fell. The storage of sufficient water to appreciably 
reduce the flood flow of large streams would require the with- 
drawal, from agricultural use, of areas of land quite dispro- 
portionate to the benefits that can possibly be secured from 
such storage. Moreover, reservoirs can seldom be located so 
as to be effective in preventing floods below a point on the 
stream where its drainage area is more than two or three times 
the area of watershed tributary to the reservoirs. Floods on 
the tributaries of a stream are practically never synchronous. 
Floods on small streams are due to excessive rains over re- 
stricted areas, and these rainstorms may center just outside of 
the reservoir controlled area, as happened during the Merrill, 
Wisconsin, storm of July, 1912, which produced a record- 
breaking flood at Wausau, Wisconsin, but hardly an appreciable 
increase in runoff from the watershed drainage into the upper 
Wisconsin River reservoirs. 

Floods on large streams result from protracted, well-dis- 
tributed rains that yield comparatively little water for storage 
at the headwaters of the tributaries where reservoir sites are 
available. To be effective in preventing floods on large streams 
reservoirs should be located a considerable distance down- 
stream on the large tributaries. In such localities, however, the 
land is usually improved and very valuable for other purposes. 

Control of Mississippi River Floods by Reservoirs. — The 
floods on the Lower Mississippi River cannot be prevented by 
reservoir storage on account of the tremendous quantities of 
water involved. This has been well stated by Col. Townsend * 
in the following words: 

"To have retained the Mississippi flood of 1912 
within its banks would have required a reservoir in the 
vicinity of Cairo, Illinois, having an area of 7000 

* Townsend, Col. C. McD., President Mississippi River Commission, in 
address before National Drainage Congress, St. Louis, Mo., Apr. 11, 1913. 



MODIFICATION OF STREAM FLOW BY STORAGE 463 

square miles, slightly less than that of the State of 
New Jersey, and a depth of about 15 feet, assuming 
that it would be empty when the river attained a 
bankful stage." 
The cost of such a reservoir would, of course, be prohibitive. 
The only economical sites for reservoirs are near the head- 
waters of the streams, and here reservoirs are relatively 
ineffective. 

The ineffectiveness of reservoirs at the headwaters of the 
Mississippi River system, for flood prevention in the lower 
reaches, is well indicated by the fact that during the 1912 flood, 
when the river at Cairo had risen about 50 feet, the upper 
Mississippi at St. Paul was contributing little more than a 
thousandth part of the flood water; the Ohio River at Pitts- 
burgh was contributing about a hundred-and-thirtieth part of 
the floodwater at Cairo; and the Missouri River at St. Joseph 
was contributing about a hundred-and-twentieth part. If all 
the water of these tributaries at the points mentioned had been 
held back by reservoirs, it would have lowered the river at 
Cairo by only a few inches during a fifty-foot flood. 

Such complete control of the upper Mississippi, the upper 
Missouri, and the upper Ohio rivers, however, cannot be ac- 
complished by even the most extensive reservoir construction, 
unless these reservoirs are to be built in populous agricultural 
communities, right outside of the large cities, and then only 
at a cost entirely incommensurate with any benefits that could 
possibly be derived therefrom. 

The small effect of the upper Mississippi River reservoirs 
on the flood flow of this stream is well indicated by the fact 
that if these reservoirs had not been in existence in 1905, the 
total natural flood flow from the lakes constituting these reser- 
voirs, at the time of the crest of the 1905 flood at Minneapolis, 
would have been less than one tenth of the total flood flow. 
The actual outflow from the reservoirs was about one half the 
natural, so that the effect of the reservoirs was to reduce the 



464 ELEMENTS OF HYDROLOGY 

flood flow at Minneapolis by less than 5 per cent. Moreover, 
in the same year (1905) these reservoirs could not even pre- 
vent a flood at Aitkin, Minnesota, on the river about 100 
miles below, much less at the Twin Cities, or at Cairo, Illinois, 
or Memphis, Tennessee. On July 1 of that year, when the 
flood at Aitkin, Minnesota, was practically at its highest, the 
reservoirs were discharging little more than their winter flow. 
The flood had been produced by the tributaries which enter the 
Mississippi between the reservoirs and Aitkin, notwithstanding 
the fact that the reservoirs control 61 per cent of the watershed 
above Aitkin. Nevertheless, during moderate floods on the 
upper river, resulting from general rains, the upper Mississippi 
Reservoirs often have an appreciable effect in reducing flood 
flow, as indicated by the hydrographs of Fig. 205. 

Engineers are agreed that flood flows on large streams cannot 
be prevented. The best that can possibly be done is tc prevent 
overflow by confining the flood waters by means of levees, and 
by straightening and enlarging the channel at critical points, 
provided the character of the material will permit increased 
velocities, or the shore protection required as the result of these 
increased velocities can be placed at reasonable expense. 

Storage for Power 

Applicability. — Irregularities in water supply make the 
storage of water for power purposes of wide applicability. The 
greatest demand for power usually occurs at the time when the 
stream flow is the lowest. Similarly, irregularities in the de- 
mand for power, both during the day and during the year, 
make storage and pondage a valuable asset of every water- 
power development. The greater the head capable of develop- 
ment at any given site the greater the value of a given amount 
of storage. While the value of a stream for power develop- 
ment purposes is usually dependent more upon its minimum 
flow than upon its average utilizable flow, yet the opportunities 
for storage are seldom sufficient to warrant the use of stored 



MODIFICATION OF STREAM FLOW BY STORAGE 465 

water entirely for increasing the dependable flow of the stream, 
as opposed to increasing its utilizable flow. In other words, 
the available storage capacity will usually yield a larger return 
on the investment if used each year for the purpose of increas- 
ing the flow of the stream up to its limit of economical utiliza- 
tion than if used for the purpose of holding water in storage 
for several years with a view to increasing the extreme low- 
water flow, and, consequently, the dependable flow which de- 
termines the maximum amount of power available at all times. 

Limit of Economical Development. — On most streams of the 
United States the variation in stream flow is so great, even 
considering all the equalization that can economically be ef- 
fected by storage, that it usually pays to install turbine capacity 
sufficient to utilize considerably more than the low-water flow. 
Just what proportion of the time water must be available to 
permit of its economical use in power development depends 
upon the relation between the fixed charges plus operating cost 
of the additional water-power plant capacity required to utilize 
water available less than 100 per cent of the time, and the 
operating cost of a steam, gas, or other auxiliary power plant. 
Merely the operating cost of the auxiliary plant should be used 
in making the comparison because this plant is required, in any 
event, to carry part of the load at time of low water. 

Size of Auxiliary Power Plant. — The size of auxiliary power 
plant required for supplementing the water-power at low water, 
without reference to insurance against interruptions in service 
from other causes, depends upon the daily variations in load 
and the storage, or more properly " pondage " available at the 
plant. When sufficient pondage is available and a plant is 
carrying the usual light and power load, the water-power plant 
can be used to full capacity during the time of peak load, and 
the steam plant can be run as nearly continuously as possible. 
With this combination, the required size of auxiliary power 
plant is usually reduced to about half of that which would 
otherwise be necessary to supplement the water-power de- 



466 ELEMENTS OF HYDROLOGY 

veloped from the low-water flow of the stream. When the 
water-supply is ample, the auxiliary plant can be used to carry 
the peak of the early evening load and the water-power plant 
run as nearly continuously, at full load, as possible. These 
considerations are basic to a proper understanding of the sub- 
ject of the modification of stream flow for water-power purposes 
by means of storage and pondage. 

The Mass Curve. — The best method of studying the effect 
of reservoir storage and pondage on stream flow is by means 
of the " mass " or " flow-summation " curve. This is a dia- 
gram which shows the net available amount of runoff or supply 
to the reservoirs, expressed in any convenient unit, which has 
accumulated in any given period of time. The slope of the 
tangent to the mass curve at any point indicates the net rate 
of runoff or inflow at that time. In summing up the runoff, the 
increment for a day, for ten days, or for a month may be used, 
depending upon the regularity in the flow of the stream and the 
available storage capacity. In the case of natural lakes the 
runoff records, that is, the outflow plus or minus storage on the 
lake, give the net inflow directly. In the case of artificial 
reservoirs the evaporation and seepage loss must first be com- 
puted and deducted from the observed or estimated runoff. 

It is particularly important that the mass curve be con- 
structed from the net available inflow, especially in the case of 
natural lakes, so as to eliminate evaporation and seepage losses 
and the effects of natural regulation. 

Two typical mass curves used in connection with the study 
of a large storage project are shown in Figs. 284 and 285. The 
volume of runoff or inflow into Rainy Lake is expressed in 
cubic feet and summed up by months. Tangents drawn to 
the mass curves at various points indicate rates of regulated 
outflow from the reservoir. Every point on these tangents 
represents the regulated outflow up to the given time and the 
point on the mass curve, directly underneath, represents the 
inflow up to the same time. The vertical distance between 



MASS CURVE OF INFLOW INTO RAINY LAKE 

, SHOWING 

REGULATION TO INCREASE DEPENDABLE OUTFLOW (METHOD A) 
Fig. 284. 




From Report of Adolpli F. Meyer ond Arthur V. While, Consulting Engineers, International Joint 
Commission, Lake of the Woods Investigation. (Data for 1915 and 1916 added by Author.) 



MASS CURVE OF INFLOW INTO RAINY LAKE 

SHOWING 

REGULATION TO INCREASE UT1LIZABLE OUTFLOW (METHOD B) 



MODIFICATION OF STREAM FLOW BY STORAGE 467 

the two points, therefore, represents the difference between 
inflow and outflow, or draft on storage. Since the area of the 
reservoir is known the draft is readily converted into reservoir 
stage, when this is desired. A full reservoir is assumed at the be- 
ginning of the period. The vertical height of the cross-hatched 
areas represents the volume of non-utilized flow or water wasted. 

Regulation to Increase Dependable Flow. — Two methods 
of utilizing the reservoir storage are shown in Figs. 284 and 285. 
Under the first method of regulation, styled " Method A," the 
aim is to utilize the available storage in securing the maximum 
possible increase in extreme low-water flow over a period of 
years, that is, to increase the dependable flow. Since it is abso- 
lutely impossible to forecast the runoff from the tributary 
watershed for any considerable time in advance, the maximum 
permissible rate of discharge, when stored water is being drawn 
upon, is limited to the dependable rate, that is, the rate which 
can be maintained on the available storage over the most ex- 
treme dry period of years to be expected. When water is being 
wasted, a higher rate may sometimes be utilized to advantage. 
In the case of Rainy Lake, the maximum rate which can be 
economically utilized is about 10,000 second-feet as turbines 
aggregating this capacity have already been installed. When- 
ever stored water is being drawn upon the outflow must be 
limited to the dependable rate or the reservoir may not be full 
at the beginning of the dry period which, in this instance, ex- 
tended over 3 years for the case of 100 billion cubic feet of 
available storage, and over 5 years for the case of 150 billion 
storage. 

Regulation to Increase Utilizable Flow. — Under the second 
method of regulation, styled " Method B," the aim is to utilize 
the available storage in securing the maximum increase in the 
ordinary low-water flow, without endeavoring to substantially 
increase the extreme low-water flow, i.e., to increase the uti- 
lizable flow. Under such regulation of stream flow the aim is 
to use as much of the available storage capacity each year 



468 ELEMENTS OF HYDROLOGY 

as possible, drawing upon the stored water at as high a rate 
as can economically be utilized by the given installation. 

Under " Method A " the available storage capacity would 
have been fully utilized only once during the 22 years. Under 
" Method B " 100 billion cubic feet of storage would have been 
fully utilized ten times in 22 years and 150 billion cubic feet 
of storage would have been fully utilized five times, but the 
reservoir would not have been full at the beginning of the ex- 
treme dry period so that during this period the reservoir 
storage would not have materially increased the natural low- 
water flow. 

Mass-curve studies which assume a variable rate of discharge 
for each dry season and are premised upon a use of all, or nearly 
all, the available storage capacity during each dry season, are 
entirely theoretical and have no practical application. They 
assume that the runoff can be accurately forecast for months 
and even years in advance. 

Frequency Curves. — Frequency curves showing the extent 
to which the outflow from Rainy Lake could have been modi- 
fied by these two methods of regulation are shown in Fig. 286. 
" Method B " results in a much greater increase in utilizable 
outflow than " Method A " but does not produce any sub- 
stantial increase in low- water flow. Even if the demand for 
power is constant, so that auxiliary power must be provided, 
" Method B " gives the better return on the investment in 
this instance. If the demand for power varies, that is, if the 
load factor is less than 100 per cent, the advantage of " Method 
B " over " Method A " increases. 

It appears from the frequency curves that, under " Method 
A," greater rates than the dependable rate would be available 
less than 50 per cent of the time and therefore hardly capable 
of economical utilization. In other words, under this method 
of regulation it usually would not pay to install greater turbine 
capacity than that required for the dependable rate, with 
possibly an additional spare unit in reserve. 



MODIFICATION OF STREAM FLOW BY STORAGE 469 











































































































































































































































































































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FREQUENCY CURVES 

SHOWING 

OUTFLOW FROM RAINY LAKE 

RESULTING FROM 

TWO METHODS OF REGULATION 

ON 100 AND 150 BILLION CU.FT. OF TOTAL STORAGE 

1892-1914 



































































































































From Report of Adolph F. Meyer and Arthur V. White, Cons. Engrs. 
International Joint Commission. 

Fig. 286. 



470 ELEMENTS OF HYDROLOGY 

When the available storage capacity is so large, however, 
as on Lake of the Woods, for example, where it aggregates about 
250 billion cubic feet, so as to make the dependable outflow 
obtainable with the given storage about 80 per cent of the 
utilizable outflow obtainable with the same storage, regulation 
according to " Method A " is preferable to regulation according 
to " Method B " because the value of the increased power 
secured from the larger installation would not compensate for 
the cost of the auxiliary power plant required under " Method 
B " to supplement the water-power at times of low water. 

Construction of Frequency Curve. — The frequency curve is 
a graph of data arranged in the order of magnitude. Any 
point on the frequency curve indicates the percentage of the 
total number of records of the given phenomenon which are 
greater than the value of this point and the percentage which 
are smaller. The point P, for example, on the frequency curve 
of Fig. 287, showing the frequency of annual precipitation at 
New Bedford, Massachusetts, from 1814 to 1913, indicates 
that 54 per cent of the total number of records of annual pre- 
cipitation were greater than 45 inches and 46 per cent were 
smaller. The portion of the curve P-O, for example, indi- 
cates that in 32 per cent of the total number of years the 
rainfall was between 40 and 45 inches. The table accompany- 
ing the diagram of Fig. 287 and the construction lines and 
dimensions on the diagram itself indicate the procedure in 
working up data into a frequency curve. The size of groups 
to be selected in subdividing data depends upon the number 
of records available and the rate of variation in the records 
as the high and low values are approached. Usually it is de- 
sirable to use smaller groups near the two extremes in values 
than in between so as to get the correct curvature for the graph. 
In order to show how nearly correct the resulting graph is the 
actual values for the 100 years records at New Bedford have 
also been plotted in Fig. 287. The smoothed curve as drawn 
undoubtedly represents the actual facts better than a curve 



MODIFICATION OF STREAM FLOW BY STORAGE 471 

which follows the observed values more closely, and will fit the 
records of 200 years better than such a curve. 




30 40 50 60 70 

Percent of Total Time (100 yrs.) 



Ordinate 


ANNUAL PRECIPITATION-INCHES 
NEW BEDFORD, MASS. 1814-1913 


67.5 


62.5 


57.5 


52.5 


47.5 


42.5 


38.75 


36.25 


33.75 


Group 


65.0 
69.0 


60.0 
64.0 


55.0 
50.0 


50.0 
54.0 


45.0 
40.0 


40.0 
44.0 


37.5 
39.0 


35.0 
37.5 


32.5 
35.0 


No. of Records 


1 







15 


29 


32 


10 


a 


1 


Cumulative 

Total 


1 


7 


10 


25 


54 


86 


96 


99 


100 


Abscissa 
(No. of Records) 


0.5 


4 


8.5 


17.5 


39.5 


70 


91 


97.5 


99.5 


Abscissa 


0.5 


4 


8.5 


17.5 


39.5 


70 


91 


97.5 


99.5 





Fig. 287. — Typical Frequency Curve Showing Method of Construction. 



472 ELEMENTS OF HYDROLOGY 

It is usually impracticable to plot the observed data in the 
exact order of magnitude. The grouping system, on the whole, 
gives better results and is incomparably faster. Where several 
thousand records are used as the basis for a frequency curve, 
no other method is practicable. 

The mean annual precipitation at New Bedford is 46.45 
inches. This amount of precipitation, however, does not occur 
with the greatest frequency and therefore is not the most likety 
to occur in any one year, that is, it is not the " normal " pre- 
cipitation. Taking the curve as the basis, annual precipitations 
of from 40 to 48| inches occur with equal frequency so that the 
normal precipitation is 44| inches, or preferably between 40 
and 48| inches. 

Frequency of occurrence in per cent, as taken off the curve, 
can readily be converted into one occurrence during an interval 
of a certain number of years. For example, a precipitation 
of 56 inches was exceeded 10 per cent of the time, that is, a 
precipitation of 56 inches was exceeded, on an average, once 
every 10 years. 

Conflict of Storage Purposes 

Perhaps no more far-reaching misconception regarding an 
engineering problem is current to-day than that the water of 
rare and extraordinary floods can be conserved and used in 
the interests of power and navigation, of flood prevention and 
irrigation, or in the interests of other combinations of two or 
three different storage purposes at one and the same time. In 
the first place, to be really worth conserving, flood water should 
be available at least once in 3 or 4 years. Flood water that 
puts in an appearance once in 10, 15, or 20 years must be 
wasted quickly and with as little damage as possible. The 
fixed charges on the cost of the structures and facilities required 
for the utilization of water which is rarely available far exceed 
any possible benefit to be derived from such use. It is safe 
to say that on no stream in the country do really destructive 



MODIFICATION OF STREAM FLOW BY STORAGE 473 

floods occur with a frequency which makes the flood water 
worth conserving. Storage for flood prevention, then, must be 
planned with that as its sole object. It does not follow, how- 
ever, that reservoirs for flood prevention and other purposes 
cannot be, in many instances, economically combined in a 
single project. In other words, instead of building several 
distinct reservoirs, the upper portion of one reservoir may be 
reserved for use in storing or retarding extraordinary floods, 
its full capacity never being exhausted, however — - not even 
once in a century. Another portion of the same reservoir may 
be in continuous use for storing water to supply the ordinary 
demands of power, navigation, or other purposes. Still another 
portion of this same reservoir storage capacity may be utilized 
for storing water that may not be required more than once in 
25 or more years, to assure a predetermined, extreme low- 
water outflow from the reservoir. A fourth portion of the 
reservoir storage may be absolutely permanent and may serve 
merely to maintain sufficient head at the outlet to permit the 
development of a certain amount of power. The last condition 
seldom prevails. It is economical to permanently store water 
for the production of head capable of use in water-power de- 
velopment, only when the area of the reservoir becomes greatly 
reduced as zero storage is approached. 

Another reason why reservoir storage designed for flood pre- 
vention cannot also be used in the conservation of water, is 
because a reservoir operated for flood prevention should be 
kept as nearly empty as possible and should not be used to store 
ordinary floods that occur every few years. Floods occur with 
great irregularity, and at different seasons. Severe rainstorms 
occasionally follow each other in rapid succession and travel 
the same paths. If reservoirs calculated to prevent floods are 
permitted to fill with ordinary flood water, there is good pros- 
pect of no storage capacity being available when the extraordi- 
nary flood occurs. 

Reservoirs operated in the interests of power, navigation, 



474 ELEMENTS OF HYDROLOGY 

and irrigation are rilled as soon as possible in spring, and the 
stored water is drawn upon only when needed. As during wet 
seasons little water need be discharged for these purposes 
such reservoirs are nearly always full when danger from ex- 
traordinary floods exists. Moreover, if natural lakes are utilized 
for storage purposes, and if no storage capacity has been specially 
reserved for flood-water storage, these reservoirs must dis- 
charge the flood water as rapidly as it runs off from the tributary 
watershed. As in large natural lakes the flood inflow is always 
greater than the flood outflow, the conversion of such lakes 
into storage reservoirs for power, navigation, and irrigation 
purposes must necessarily increase extreme floods on the river 
below unless provision is made in the same project for storing 
the extreme flood-water runoff. 

Storage Below Ordinary High-water Mark 

On navigable lakes and rivers the Government of the United 
States holds an easement to use the riparian lands up to or- 
dinary high-water mark, in the public interest. The right to 
use such lands is often granted to private corporations in con- 
nection with projects for water-power development that also 
further the public interest of navigation. Moreover, the 
Supreme Court of the United States has held * that Congress 
intended to provide that the common-law rules of riparian 
ownership should apply also to lands bordering on non-navi- 
gable streams. It is of interest, therefore, to consider the 
possibilities and the limitations of modifying the flow of streams 
by storage below ordinary high-water mark. 

Ordinary High Water Defined. — References to some im- 
portant court decisions defining ordinary high water appear 
below. t The gist of these decisions is that where the banks 
of a body of water are relatively steep, ordinary high-water 

* Railroad Co. vs. Schurmeier, 74 U. S. 272. 

t In re Minnetonka 56 Minn., 513, Erdman vs. Power Co., 112 Minn., 175 
Dorman vs. Ames, 12 Minn., 457. 



MODIFICATION OF STREAM FLOW BY STORAGE 475 

mark " is coordinate with the limit of the bed of the water; 
and that, only, is to be considered the bed which the water 
occupies sufficiently long and continuously to wrest it from 
vegetation, and destroy its value for agricultural purposes." 
When the banks are low and flat, ordinary high-water mark 
is to be considered " the point up to which the presence and 
action of the water is so continuous as to destroy the value 
of the land for agricultural purposes by preventing the growth 
of vegetation, constituting what may be termed any ordinary 
agricultural crop, — for example, hay." All stages that are 
" usual, ordinary, and reasonably to be anticipated " are within 
ordinary high -water mark but not " such extraordinary freshets 
as cannot be reasonably anticipated at particular periods of the 
year." 

In most instances, ordinary high-water mark is difficult to 
determine. The extent to which land at a given elevation, 
bordering a body of water, is valuable for agricultural purposes, 
and the character of the vegetation found upon this land, varies 
from year to year, with the rainfall and other climatic con- 
ditions. If, in view of this fact, a conclusion respecting the 
possible agricultural use of riparian land must be premised upon 
records of meteorological phenomena, or of prevailing levels 
under natural conditions, extending over a considerable period 
of years, a definition of " ordinary high- water mark " directly 
in terms of observed hydrological phenomena must sooner or 
later find acceptance. The author has used the two following 
definitions in his practice. The results derived through the 
application of these definitions to a given group of data usually 
do not differ widely. According to the first definition, ordinary 
high water is the average of all stages above the average stage 
which prevailed during the agricultural season — that is, the 
planting, growing, and harvesting season. According to the 
second definition, high stages during the agricultural season 
are all those stages which are higher than the stage which was 
exceeded just 50 per cent of the time. Of the high stages, 



476 ELEMENTS OF HYDROLOGY 

ordinary high-water mark corresponds to that stage which was 
exceeded one half the time. In other words, ordinary high- 
water mark corresponds to that stage of a lake or a river which, 
on an average, was exceeded 25 per cent of the time during the 
agricultural season. As in other matters, judgment must be 
exercised in the application of these definitions to prevailing lake 
stages, and particularly to river stages. 

Storage Limitations. — The extent to which stream flow can 
be regulated within ordinary high-water mark has unquestion- 
ably been greatly over-estimated. If, in the usual case of 
maximum natural inflow into a lake exceeding the maximum 
natural outflow, such a lake is held at ordinary high-water 
mark without increasing its outflow capacity, riparian property 
around the lake will be damaged during extreme high water, 
because the lake level is continuously higher than it would 
have been under natural conditions. If, now, the outflow 
capacity is increased so as to prevent the level of the lake, 
under any given flood conditions, from rising any higher than 
it would have risen, under the same hydrological conditions, 
with the outlets in a state of nature, the flood-water discharge 
from the lake will produce a stage in the channel below the 
outlet which will exceed the natural ordinary high-water mark. 
In other words, regulation of lake levels or modification of 
stream flow by storage below ordinary high-water mark is a 
physical impossibility. 

When the banks of the channel below the outlet of the lake 
are high the damage from the greater flood-water discharge 
under regulation within ordinary high-water mark on the lake 
above may be negligible, even though the high-water mark in 
the channel below is considerably exceeded. Every case, how- 
ever, must be considered on its own merits. Not infrequently, 
flowage rights must be secured both in the lake and on the dis- 
charge channel below the outlet. 



MODIFICATION OF STREAM FLOW BY STORAGE 477 

NOTE TO TEACHERS OF HYDROLOGY 

The author has purposely refrained from adding questions 
and problems to the several chapters of this book. An engi- 
neer who is qualified to teach the subject should also be quali- 
fied to frame intelligent and instructive questions. There are 
few colleges in which exactly the same amount of time is de- 
voted to this subject. Usually the work is scattered through 
a half dozen different courses. The author believes that there 
is nearly as much reason for teaching hydrology as a funda- 
mental course, instead of scattering the instruction through 
courses in water-supply, water-power, sewerage, drainage, irri- 
gation, etc., as there is for teaching mathematics as a funda- 
mental course. In view of this, an effort has been made to 
present the elementary subject-matter, accompanied by various 
methods of analyzing and interpreting data, and through these 
the elucidation of the fundamental principles of hydrology. 
It is not intended that assignments should be made page by 
page, although an effort has been made to develop the subject 
in a logical manner. Minor details have been omitted, and 
ample opportunity has been left for the work of the individual 
instructor. 

A clear understanding of the factors that modify the flow 
of streams is absolutely essential to an intelligent use of stream- 
flow data. The author knows of no better way to crystallize 
the student's knowledge of these factors than to permit him 
to apply that knowledge in computing runoff from rainfall 
and other physical data. Watersheds coming within the 
student's observation should preferably be selected. Complete 
physical data should be available, including runoff records for 
at least a few years. To enable the students to fully grasp 
the work, the author takes them by groups and goes through 
the complete computations with them. When the classes are 
large, appointments are made so that one student is taken into 
the group and one excused about every hour, thus maintaining 



478 ELEMENTS OF HYDROLOGY 

a continuous organization of from 4 to 6 men, throughout an 
afternoon, for example. Each student first collects the neces- 
sary data and makes the preliminary evaporation and tran- 
spiration computations for one year. These data and com- 
putations are then taken in chronological order and the monthly 
runoff computed by the students in groups of four to six men, 
the instructor preferably taking the computation sheet in hand 
himself and assigning to the several students, in rotation, the 
daily temperature and precipitation records, the curves of 
surface and seepage flow, etc. Each student, under the super- 
vision of the instructor, teaches his successor the work which 
he in turn is to do. Students not engaged on this work spend 
their time on other assignments until the computations for the 
entire period have been completed. A comparison is then 
made of computed with observed runoff, in case the funda- 
mental curves of surface and seepage flow, etc., had been pre- 
viously worked out by the instructor, and existing discrepancies 
analyzed with a view to determining the cause. The computed 
data, combined with such records of observed runoff as are 
available, are then used in the construction of a mass curve 
extending over at least twenty years, if possible, from which 
a study is made of different methods of modifying stream flow 
by reservoir storage. 



INDEX 



Air, dynamic cooling of, 61, 64 

effect of vapor on weight, 62 

stable and unstable, 62 

see also "Atmosphere" 
Alvord, John W., 321 
Arkansas River, 351 
Artesian water, basins, 264-268, 321 

reservoirs, 263, 264 

temperature of, 264 
Ashokan reservoir, capacity, 438 

cost, 438 
Atmometer, porous cup, 206 
Atmosphere, absorption of solar radi- 
ation by, 17, 18 

circulation, 34-38 

composition, 9 

distribution of gases, 10 

height of, above earth's surface, 11 

properties, 11 
density, 55, 56 
pressure, 27-31 

see also "Barometric pressure" 
specific heat, 11, 56 

use, 9 

see also "Air" 

Barometric pressure, amount of, 27, 
28 

as aid in forecasting weather, 78 

daily variation, 30, 31 

effect of, on rate of evaporation, 
192, 198, 199, 200 

effect of, on seepage flow, 289 

effect of, on state of water, 38 

effect, on wind velocity, of differ- 
ence in, 66 

high and low pressure areas, 29, 70, 
71 

measurement of, 27, 28 

reduction of, during tornado, 34, 35 

variation of, with altitude, 27-29 



Bazin's formula, 396 
Beaulieu, Minnesota, storm, 133, 139 
Bigelow, Frank H., 30, 71, 191, 192, 
195 
•evaporation formula, 197, 201, 203, 
204 
Binnie, Sir Alexander, 93 
Birkinbine, Carl P., 88 
Bixby, Gen. W. H., 455 
Black River, 308, 313, 341 
Briggs, Lyman J., 234, 250, 258, 259 
Brooks, Chas. F., 87 
Burdick, Charles B., 321 
Butcher, W. E., 400 

Cairo, Illinois, storm, 137, 138, 139 

Cane Creek flood, 348 

Capillary water, 231-235, 249-254 

Cedar Lake Reservoir, 440 

Cedar River flood, 326 

Chandler, E. F., 207, 335 

Check dams, 456, 457, 458 

Chemical method of measuring flow 

of water, 400, 401 
Chezy's formula, 394 
Chinook winds, evaporation during, 

219 
Clearwater River, 307 
Clements, F. E., 242 
Colorado River, runoff, 297, 436 
Conway, G. R., 350 
Croton River, 412, 450 
Crow River, 366 
Crow Wing River, 307, 310, 312, 327, 

340 
Cultivation, effect of, on runoff, 188, 

281 
effect of, on percolation, 229, 230 
Current meter, Haskell, 375-377, 381, 

382 
measurements, 382, 384, 385 



479 



480 



INDEX 



Current meter, measurements, field 
and office notes, 385, 3SG 

Price, 375-377, 381, 382 

rating of, 377, 378, 379 

section, 368, 369, 370 
Cyclonic weather, 29 

average velocity of cyclones, 70 

characteristics of, 29, 65-71 

occurrence of thunderstorms dur- 
ing, 71 

precipitation during, 65, 66 

wind accompanying, 36 

Dalton's law, 191, 201, 209 
Dewpoint hygrometers, 49, 50, 51 

temperature, 53, 190 
Diaphragm method of measuring 

stream flow, 403, 404 
Drainage, effect of, on evaporation 
opportunity, 237, 238 
effect of, on runoff, 282, 283 

Elk River, 307, 310, 313, 318 
Evaporation, definition of, 190 

effect of, on low-water stream flow, 

358, 359 
from land areas, 221-241, 426 
author's curve for, 421, 423 
effect of relative humidity, 224 
effect of temperature, 221-224 
effect of vegetation, 225, 226 
irrigation investigations, 238, 239 
observed, 238, 240 
opportunity, 226-241 

capillary lift of soils, 231-233 
effect of depth of water-table, 

235, 236 
effect of drainage, 237, 238 
effect of interception, 227 
effect of percolation, 228 
effect of precipitation, 226 
effect of vegetation, 236, 237 
from snow and ice, 218, 219 
from water surfaces, 188-220, 425, 
426 
effect of barometric pressure, 192 
effect of relative humidity, 194, 

195 
effect of temperature, 190, 191 



Evaporation, from water surfaces, 
effect of wind velocity, 38, 
195, 196, 197 
formulas, Dalton's, 191, 192 
Bigelow's, 198 
Russell's, 199, 200, 201 
comparison of, 201 
measurement of, evaporation 
pans, 205 
correction for size of pan, 204 
Piche evaporometer, 199-201 
porous cup atmometer, 206 
observed, Boston, Mass., 207, 
208, 210 
Grand River Lock, Wis., 206, 

208, 209 
Independence, Calif., 207, 208, 

211 
Kingsburg, Calif., 207, 208, 

210 
Lee Bridge, England, 207, 208, 

211 
Mount Hope, N. Y., 212 
University, N. D., 206, 208, 209 
from deep water, 214, 216, 220 
from shallow water, 209, 212, 
220 
losses from reservoirs, 439, 451 
losses in channels, 449 
relative, from land and water areas, 
239, 240 

FitzGerald, Desmond, 195, 208 
Float measurements, applicability, 
392, 395 
surface floats, 394 
subsurface floats, 394 
rod floats, 394 
Floods, due to heavy rains, 318-324 
due to snowfall, 326-333 
effect of cultural conditions, 313 
effect of open ditch drainage, 281 
effect of precipitation, 309, 318- 

321, 323, 324, 329 
effect of soil, 313 
effect of temperature, 329 
effect of watershed area, 310, 311 
effect of watershed shape and loca- 
tion, 311, 313 



INDEX 



481 



Floods, estimates of probable, 310, 
320, 321 
formulas for, 341-347 
prevention, 455, 463 

control of Mississippi River, 462, 

463 
conflict with other purposes, 

472-474 
methods of, 456 

check dams, 456, 457 
retarding basins, 458 
impounding reservoirs, 461, 
462 
typical winter and spring, on large 

streams, 351-357 
Cane Creek, N. C, 348 
Crow Wing River, 327 
Elk River, 314, 318 
Great Miami, 356 
Heppner, Ore., 348 
Hudson River, 345 
Little Fork River, 327, 340 
Minnesota River, 340 
Mississippi River, 332, 333, 351, 

353 
Monterey, Mexico, 349 
Ohio River, 329, 330, 331, 353, 354, 

355 
Passaic River, 341 
Red River of the North, 335 
Root River, 314, 341 
Scioto River, 355, 356 
Seine River, 356, 357 
Wild Rice River, 316, 320, 321 
Forecasting weather, 77, 78 
Forests, effect of, on flood flow, 313, 
326, 327, 329 
effect of, on low-water flow, 358 
effect of, on surface runoff, 281, 282 
evaporation from, 225, 226 
relative humidity in, 224 
temperature in, 223, 224 
transpiration of, 261, 262 
For tier, Samuel, 442 
Fort Madison, Iowa, storm, 134, 139, 

320, 321 
Frequency curves, 346, 347, 468 

construction of, 470, 471 
Fuller, Weston E., 342 



Gages, automatic recording, 371, 373, 
374 
chain, 370, 371 
hook, 370 

rain, see "Rain gages" 
staff, 370 
Gaging station, 368 
Groat, B. F., 377, 402, 405 
Ground-water, effect of, on low-water 
flow of streams, 358, 361, 362 
loss from reservoirs, 443, 445 
see also "Seepage," "Gravity 
water, " " Capillary water ' ' 
and "Water-table" 
Grover, N. C, 390 
Grunsky, C. E., 204, 208 
Greaves, Chas., 208 
Grain fields, evaporation from, 226 
transpiration from, 262 
see also "Vegetation" 
Grasses, evaporation from grass land, 
226 
root systems of, 254, 256, 257 
transpiration of, 261, 262 
see also "Vegetation" 
Gravity water, amount of, in soils, 
249-253 

Hann, Dr. Julius, 23, 29, 30 
Hardy, Arkansas, storm, 135, 136, 139 
Hazen, Allen, capillary lift of soils, 
232 
flow of water through soil, 269, 

270, 274 
over-registration of Venturi meters, 

408 
storage for municipal water supply, 
450 
Heat, absorption of, by land and 
water areas, 14 
of vaporization, 42 
of fusion, 42 
source of, 13 
Henry, A. J., 354 
Herschel, Clemens, 406 
High-water mark, defined, 474, 475 

storage below, 474 
Hillberg, A. G., 396 
Hopson, E. G., 440 



482 



INDEX 



Horton, R. E., 81, 219, 221, 326, 345, 

396 
Hoyt, John C, 390 
Hoyt, W. G., 360, 364, 392 
Hubbard, W. D., 443 
Humphreys and Abbot, 394 
Humphreys, W. J., 9 
Hydrographs of typical streams, 299- 

309, 311* 
Hydrology, definition of, 1 

application of, 2-4 

present state of, 1-2 

subject matter of, 5-8 
Hygrometer, direct, 44, 45 

indirect, 45 

wet- and dry-bulb, 50, 51 

Ice, anchor, 41 

evaporation from, 218, 226 

effect of formation of, on stream 
flow, 360, 361, 362, 391, 392 

frazil, 40, 41 

formation of, 40, 41, 214, 216 

heat of fusion, 42 

storms, 87, 88 
Interception of precipitation, 227, 228 
Irrigation, investigations, 238, 239 

reservoirs, 451, 452 

Kennison, K. R., 394 
Kiersted, W., 443 
Kiesselbach, T. A., 246 
King, F. H., 228, 232, 272, 289 
Kuichling, Emil, 342, 362 
Kutter's formula, 321 

variation of different factors in, 394 

Lakes, effect of, on flood flow, 321 
effect of, on low-water flow, 359, 

360 
effect of, on runoff, 283, 284 
temperature of, 214 
Lee, Chas. H., 208, 233 
Little Fork River, 313, 327, 340 
Livingston, B. E., 206, 258 
Low-water flow of streams, effect of 
ground-water supply, 358 
effect of lake and swamp storage, 
358, 359 



Low-water flow of streams, effect of 
precipitation, 358 
effect of reservoir storage, 453, 454 
effect of temperature, 360-363 
observed, 362, 364, 365, 366 

McCulloh, Walter, 450 
McGee, W. G., 234, 235 
Marsh, evaporation from, 225 
effect of, on runoff, 281, 286 
Marvin, C. F., 44, 45 

float gage, 80 
Mass curves, of temperatures above 
freezing, 335, 337, 338-341 
use of, in storage studies, 466, 467 
Mead, D. W., 265, 414 
Mellet, R., 402 
Merrill, Wis., storm, 141, 142 
Miami River, 355, 356 

flood prevention on, 458 
Minnesota River, runoff, 297, 337, 

338, 340 
Mississippi River, effect of low tem- 
peratures on runoff, 361, 362 
effect of watershed area on runoff, 

310, 311 
floods at St. Paul, 332, 333 
floods on lower reaches, 351, 353 
rod float measurements of, 393, 395 
subsurface float measurements of, 

394 
temperature and rainfall on water- 
shed of, 297 
variation in rainfall and runoff, 
410-413 
Mississippi River reservoirs, capacity, 
437, 453 
control of floods by, 462, 463, 464 
cost of, 437, 438 
effectiveness in aiding navigation, 

453, 454, 455 
seepage loss, 443 
Monterey, Mexico, flood, 349 
Montgomery, E. G., 246 
Moore, Sir John, 26 
Moore, W. L., 17, 34 
Morgan, Arthur E., 142 
Mount Weather, solar radiation re- 
ceived at, 15, 16 



INDEX 



483 



Navigation reservoirs, applicability, 
452, 453 
Russian system, 453 
upper Mississippi River system, 453 
effectiveness of, 453, 454, 455 

Normal, definition of, 114, 121, 347 

Ohio River, runoff from watershed 
above Wheeling, 297 
floods on, 321-325, 329-332, 340, 
351, 353, 354, 355 

Olmsted, F. H., 456 

Ottertail River, 307, 386 

Passaic River, 341 

Percolation, change in seepage flow 
following, 287 
effect of, on evaporation oppor- 
tunity, 228 
effect of ponds on, 283, 284 
into rock strata, 263-269 
rates of, 228, 229 
soil moisture available for, 251 
Pit River, runoff, 298, 299 
Pitot tube, 404-406 
Pitometer, Cole, 406 
Polar regions, annual temperature, 
variations in, 19 
daily atmospheric pressure, varia- 
tions in, 29, 30 
daily temperature, variation in, 22 
hours of daylight, twilight, and 
night in, 18 
Ponds, effect of, on runoff, 283, 284, 

286 
Power, storage of water for, see 

"Reservoirs" 
Precipitation, annual, 64 
cycles in, 93, 94, 110 
maps of maximum and minimum, 

112, 113 
map of mean, 93 
relation between length of record 

and extremes of, 93 
records of, at typical stations, 
Astoria, Oregon, 104 
Boston, Mass., 94 
Cincinnati, O., 96 



Precipitation, annual, records of, El 
Paso, Texas, 103 
Havre, Mont., 102 
Marietta, O., 97 
New Bedford, Mass., 94 
New England States, 95 
New Orleans, La., 100 
Portsmouth, O., 96 
Providence, R. I., 95 
Salt Lake City, Utah, 102 
San Diego, Calif., 103 
San Francisco, Calif., 103 
Savannah, Ga., 99 
St. Louis, Mo., 101 
St. Paul, Minn., 101 
Upper Ohio River Valley, 97 
Washington, D. C, 98 
convective, 65 
cyclonic, 65, 66 

effect of, on evaporation oppor- 
tunity, 226 
effect of increase of evaporation on, 

188 
effect of, on transpiration, 256, 257 
estimating probable maximum, on 

watersheds, 141, 142, 143 
excessive rates of, 122 
daily, 122, 123 

records of, 124-127 
hourly, 144 
intense, 152-187 

comparison of formulas for, 186, 

187 
frequency of recurrence of, 176- 

185 
records of, 145-187 
irregular occurrence of, in the 

United States, 89 
lack of direct relation to runoff, 

415-421 
monthly, 114 

determination of true mean, 121, 

122 
excessive, 122, 123 
records of, 127, 128 
frequency of recurrence of, 122, 
123 
measurement of, 78 
orographic, 65 



484 



INDEX 



Precipitation, relation of, to number 
of thunder-storms, 73 
relation of, to temperature, 73, 86- 

88, 188 
variation with latitude, altitude, 

88, 89 
variation on typical watersheds, 
410, 411, 412 
Psychrometers, 51 

Rafter, G. W., 416, 418 
Rainfall, see "Precipitation" 
Rain gage, exposure of, 80, 81 
Marvin, 80 
standard, 78, 79 
tipping-bucket, 79, 80 
Rainy Lake, frequency curve of out- 
flow, 468 
mass curve of inflow, 466, 467 
Red Lake River, 307 
Red River of the North, 311, 313, 

340 
Relative humidity, 53 

effect of, on evaporation, 194, 195, 

224 
variation with altitude, 27, 28 
variation with season, 53 
variation with temperature, 53 
Relief map, of the United States, 426, 

427 
Reservoirs, applicability dependent 
on cost, 437 
characteristics of good site for, 438 

dam site, 441 
conflict of storage purposes, 472- 

474 
effectiveness, 311, 441-449 
evaporation losses from, 439 
flood prevention, 455-462 
for improving sanitary conditions, 

450 
increasing low-water flow, 429 
irrigation, 451, 452 
logging, 452 

Mississippi River, 462-464 
municipal water supply, 449 
navigation, 452-455 
power, applicability, 464, 465 
frequency curves, 468 



Reservoirs, power, limit of economical 
development, 465 
mass curve, 466, 467 
regulation to increase dependable 

flow, 467 
regulation to increase utilizable 

flow, 467, 468 
size of auxiliary plant, 465, 466 
sedimentation of, 441 
seepage losses from, 439 
spillway capacity, 440 
storage below ordinary high-water 
mark, 474-476 
Retarding basins, 458, 459 
Root River, 307, 313, 314, 319, 340, 

341, 366, 429, 432 
Rum River, 311 
Runoff, definition of, 279 

from typical watersheds, 297, 298 
methods of computing from physi- 
cal data, 414-417 " 
author's method, 424-436 
relation of, to evaporation, 189 
seepage flow, changes of, following 
percolation, 287 
effect of character of precipita- 
tion on, 286 
effect of watershed characteris- 
tics on, 285, 286 
loss, 263 
surface flow, effect of drainage on, 
282, 283 
effect of lakes and ponds on, 283, 

284 
effect of physical characteristics 

of watersheds on, 280 
effect of precipitation and tem- 
perature on, 279, 280 
variation of, on Mississippi River 
and Tohickon Creek water- 
sheds, 410, 411, 412 
see also "Stream Flow," "Floods," 
"Low- water Flow" 
Russell, evaporation formula, 192, 
198, 199, 200 

St, Croix River, runoff, 297 
Sacramento River, runoff, 298, 299 
Sand, evaporation from, 225 



INDEX 



485 



Sand, percolation through, 228, 229 

see also "Soil" 
Santa Catarina River, 349 
Sargent, Edward H., 412 
Scioto River, floods on, 321, 35G 
retarding basins on, 458, 459 
Sedimentation of reservoirs, 441 
Seepage flow, change in, following 
percolation, 287 
computation of, 432 
effect of drainage, 282, 283 
effect of temperature, 361 
effect of watershed characteristics, 

285, 286 
measurement of underflow, 276, 

277, 278 
motion of underground water, 268- 

274 
relation to low-water flow of 

streams, 358 
retardation of, 445 
underground reservoir, 263, 264 
Seepage losses, in conveying chan- 
nels, 441, 442, 443 
from reservoirs, 439, 451 
Seine River, 356, 357 
Shantz, H. L., 250, 258, 259 
Shenehon, Francis C, 370 
Sherman, C. E., 142 
Siemens, William, 248 
Simpson, Dr. G. C, 71 
Slichter, C. S., 234, 264 

formula for flow of water through 

soil, 272, 273, 274 
method of measurement of under- 
flow, 276 
Snow, 64 

accumulation of, 325, 326 
determining water content of, 82, 

. 84 
evaporation from, 218-220 
floods due to, 78, 79, 226-241 
measuring fall of, 86 
melting of, 326, 327, 429-431 
surveys, 85, 86 
Soil, capillary lift of, 230-235, 249 
formation of alkali, 234 
capillary water in, 230-232, 249-254 
classification of grains of, 250, 251 



Soil, determining moisture content of, 
under field conditions, 253 
effect of character of, on evaporation 
loss, 240 
on flood flow, 313, 327 
on natural vegetation, 256 
on seepage flow, 284, 285 
on surface runoff, 281, 432 
effect of soil moisture on transpira- 
tion, 249 
flow of water through, 268-278 
Hazen's formula, 269 
Slichter's formula, 272-274 
gravity water in, 249 
heat absorption and reflection by, 

14 
rates of percolation in, 229, 230 
typical of arid region, 442, 443 
Solar radiation, 13 

absorption of, by atmosphere, 18 

amount received, 15 

effect of forest fires and volcanic 

eruptions on, 15 
effect of water vapor on absorption 

of, 14-18 
measurement of, 15 
variation of, 14, 15 
Soundings, methods of making, 369, 

370 
Specific heat, of the atmosphere, 11, 
56 
of water, 42 
of water vapor, 1 1 
Spillway, required capacity of, 440 
Stabler, Herman, 441 
Stefan formula, effect of barometric 
pressure on evaporation, 
192 
Stewart, C. B., 141, 142 
Stewart, J. B., 234 
Storage, see "Reservoirs" 
Storms, areas covered by, 129-139 
average velocity of, 70 
exceptional, 149 
ice, 87, 88 
paths of, 139, 354 
typical excessive, at Beaulieu, 
Minn., 128, 129, 132, 133 
at Cairo, 111., 132, 138, 139 



486 



INDEX 



Storms, typical excessive, at Fort 
Madison, la., 130, 134, 139, 
320 
at Hardy, Ark., 131, 132, 135, 
136 
Stream-flow, data from power plants, 
368, 408, 409 
discharge curves, 382, 386, 389, 390 
effect of ice on, 391, 392 
mean velocity, 379-382 
measurement of, 382-385 
chemical method, 400-403 
current meter, 364, 375, 376, 377 
diaphragm, 403, 404 
floats, 392, 394, 395 
Pitot tube, 404, 405 
traveling screen, 403, 404 
Venturi meter, 406, 407, 408 
modification of, by storage, see 
"Reservoirs" 
Swamps, evaporation from, 225 
effect on runoff, 281, 286, 307, 358, 
359, 360 

Tate, Thomas, 193 
Temperature, 13-27 
annual variation, 22 
at spring break-up, 220 
daily, 21, 22 
data, 19 

data required for runoff computa- 
tions, 424, 425 
effect of, on evaporation, 190, 221 
effect of, on flow of water through 

soil, 270, 271, 273, 361 
effect of, on runoff, 297 

on flood flow, 326, 329, 330, 333, 
335 

on low-water flow, 360-362, 366 
effect of, on state of water, 39 
extending short-term records of, 27 
extremes of, 23 

map of maximum recorded, 24 

map of minimum recorded, 25 
mass curves of, 335, 337 
measurement of, 19 
of artesian water, 264 
of dewpoint, 53, 190 
periodic variation in, 23 



Temperature, relation to amount of 
water vapor, 12, 13 

variation with altitude, 23-28, 31 

variation of character of precipi- 
tation with, 86, 87 

of deep lakes, 214-216 
Thermograph, 21 
Thermometers, maximum, 19 

minimum, 21 

recording, 21 
Thief River, 307 
Thunderstorms, 71-73 
Tohickon Creek, runoff, 297 

variation in rainfall and runoff, 
410-413 
Tombigbee River, runoff, 297 
Townsend, Col. C. McD., 462, 463 
Transeau, E. N., 225 
Transpiration, amount of, 259, 260 

base curve of, 244, 424 

computation of, 426 

definition of, 242 

effect of character of vegetation, 
254 

effect of humidity, 246 

effect of light, 246, 247 

effect of precipitation, 256, 257 

effect of soil moisture, 249 

effect of temperature, 242-245 

effect of wind, 246 

effect of, on low-water flow of 
streams, 358 

observed, 238 

proportional to dry matter pro- 
duced, 258, 259 
Tuolumne River Reservoir, 441 

Van Hise, C. R., 263, 264 

Van Ornum, J. L., 437 

Van't Hoff's law, 242 

Vapor, see "Water vapor" 

Vaporization, heat of, 42 

Vapor pressure, 43, 48 

effect of, on rate of evaporation, 

190-192, 198, 199 
variation of, with temperature, 49 
see also "Relative humidity" 

Vegetation, effect of character of, on 
transpiration, 254, 262 



INDEX 



487 



Vegetation, effect of precipitation on 
character of, 256 
effect of, on evaporation oppor- 
tunity, 236, 237 
effect of, on rate of evaporation, 225 
rapid growth of, 17 
water requirements of, 257, 258, 
259 
Velocity curves, 380, 382 
Velocity of approach, 408 
Venturi meter, 407, 408 
Vermeule, C. C, 414 

Waldo, Frank, 18 

Water, as a natural resource, 5 

capillary, 231-235, 249-254 

composition of, 39 

cycle of, 5, 188 

effect of barometric pressure on 
state of, 38 

effect of temperature on state of, 39 

elasticity of, 41 

physical properties of, 39, 41, 42 

weight of, 41 
Water-table, depth of, 235, 236, 289 

desirable location of, for reservoir 
sites, 439, 440 

relation to low-water flow, 358, 361 
Water vapor, amount of, in atmos- 
phere, 9, 11, 12 

characteristics of, 43 

condensation of, 61, 64- 66 

density of, 11 

distribution of, 12, 13, 44 

effect of, on solar radiation, 14 



Water vapor, effect of, on weight of 
air, 62 

measure of, 44, 45, 50, 51 

pressure of, 43-48 

specific heat of, 11 

variation of, with altitude, 13, 27, 
28 

weight of, 11 
Water year, 417-421 
Weather, Bureau, 15, 19, 27 

cyclonic, see "Cyclonic weather" 

forecasts, 77 

maps, 77 

observation stations, 19 
index map of, 150, 151 
Wells, breathing of, 289-291 

depth to water in, 266, 268 
White, W. M., 402, 403 
Whitney, Milton, 234 
Wild Rice River, 320, 321 
Wilting coefficient, 249 
Wind, as aid in weather forecasting, 
77, 78 

cause of, 35 

effect of, on rate of evaporation, 
195-200 

effect of, on transpiration, 246 

periodic and non-periodic, 36 

pressure of, 34 

protection of rain gage from effect 
of, 80, 81 

velocity of, 34, 35, 66 

zones, 35 
Wisconsin River, 308, 313 
Wollny, E., 229, 236 







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